High-precision light pillar display method and system based on liquid crystal variable refractive index

Abstract

The invention discloses a high-precision light column display method and system based on a liquid crystal variable refractive index, and the method comprises the steps: generating a multi-dimensional driving signal with a spatial gradient characteristic according to a preset spatial distribution parameter of a target light column, and carrying out the coupling regulation and control of the voltage amplitude and frequency of the multi-dimensional driving signal, the molecular arrangement state of the liquid crystal electro-refractive index adjusting layer is dynamically changed, and a refractive index gradient field matched with the axial phase distribution requirement of the light column is established. Through a waveguide mode-phase field discretization cooperative mapping mechanism and a double-loop dynamic anti-interference architecture, real-time generation of a high-resolution light beam and stable transmission in a complex environment are realized without a mechanical scanning part, and high precision and strong robustness are achieved.

Description

Technical Field

[0001] This application relates to the field of high-precision light column display technology, and particularly to a high-precision light column display method and system based on liquid crystal variable refractive index. Background Art

[0002] Light column display technology plays a key role in fields such as three-dimensional holography, optical manipulation, and augmented reality. Its performance core depends on the precise control of the beam phase distribution and transmission stability. However, the existing technology is subject to the dual limitations of physical mechanisms and system design, facing the following challenges: 1. Traditional liquid crystal light column regulation schemes design drive signals based on a continuous refractive index model. However, actual optical waveguides (such as photonic crystal waveguides) only support the transmission of discretized Bloch modes due to the constraints of periodic structures. This physical property leads to a mismatch between continuous phase modulation and waveguide eigenmodes, causing the leakage of optical field energy to non-target modes during transmission, seriously damaging the spatial continuity of the light column.

[0003] 2. Polarization-phase cross-interference Under dynamic perturbations, the strong coupling characteristics between the polarization state and transmission mode in the optical waveguide cause polarization dispersion to be induced by the birefringence effect due to environmental temperature changes, mechanical vibrations, etc., which in turn distorts the phase distribution. Existing methods usually adopt static compensation or single-dimensional regulation (such as only correcting the voltage amplitude), and cannot cope with the non-linear coupling effect between polarization and phase in dynamic scenarios, ultimately resulting in irreversible distortion at the edge of the light column.

[0004] In current technologies, although the mechanical scanning-based phase modulator can partially improve the resolution, its response speed and system complexity are difficult to meet the requirements of real-time interaction; while the traditional electro-controlled liquid crystal scheme has the advantage of fast response, but due to the single driving dimension (only voltage amplitude regulation) and open-loop control architecture, it cannot balance the mode matching accuracy and dynamic anti-interference ability. Summary of the Invention

[0005] To solve the above problems, an embodiment of the present invention provides a high-precision light column display method based on liquid crystal variable refractive index. The method includes: Generating a multi-dimensional drive signal with spatial gradient characteristics according to the preset spatial distribution parameters of the target light column, and dynamically changing the molecular arrangement state of the liquid crystal electro-optic refractive index adjustment layer through the coupled regulation of the voltage amplitude and frequency of the multi-dimensional drive signal, to establish a refractive index gradient field that matches the requirements of the axial phase distribution of the light column; Coupling the incident light beam into the total reflection transmission channel of the optical waveguide structure, performing spatial phase modulation on the transmitted light beam based on the refractive index gradient field, and generating a discretized base optical field adapted to the geometric constraint conditions of the optical waveguide structure through the geometric boundary constraint effect of the optical waveguide structure; Apply polarization state synchronous control to the discretized base optical field, dynamically correct the polarization dispersion angle deviation of each diffraction order using the birefringence compensation algorithm, and generate an Nth-order controllable diffraction optical field with a fixed phase relationship through multi-stage diffraction synthesis; Introduce the Nth-order controllable diffraction optical field into the free space propagation domain, realize the spatial superposition of each order diffraction field through the Fresnel diffraction integral, reconstruct a continuous and high-precision light column shape, and use the wavefront distortion amount detected by the light column edge detection feedback to inversely correct the voltage control parameters of the drive signal to form a dynamic closed-loop calibration mechanism.

[0006] Furthermore, the multi-dimensional drive signal generation method includes: Establish a transfer function matrix of drive voltage and phase modulation according to the Bloch mode eigen-equation of the optical waveguide structure; Perform an inverse operation on the transfer function matrix through a feedforward neural network to generate a pre-distorted drive signal including inter-mode coupling compensation; Load the pre-distorted drive signal onto the traveling wave electrode of the electro-optic modulator to form a refractive index gradient field with a spatio-temporal distribution.

[0007] Furthermore, the optical waveguide structure is a photonic crystal waveguide, and the optical waveguide structure includes: A hexagonal close-packed air hole array arranged periodically along the propagation direction, and the duty cycle of the air holes matches the group velocity distribution of the Bloch mode; A graded refractive index cladding covering the waveguide sidewall, and its refractive index is distributed in a hyperbolic secant function along the radial direction, which is used to constrain the paraxial propagation characteristics of the refractive index gradient field.

[0008] Furthermore, the polarization state synchronous control method includes: Integrate a polarization beam splitter at the input end of the photonic crystal waveguide to decompose the incident light into TE mode and TM mode orthogonal polarization components; Apply the odd and even channel voltages in the pre-distorted drive signal to the TE mode and TM mode respectively; Through the time-domain interleaved scanning method, make the birefringence delay amounts of the orthogonal polarization components form a complementary distribution in space.

[0009] Furthermore, the wavefront distortion amount detection method includes: Collect the diffraction spots of the orthogonal polarization components using the output end of the polarization beam splitter; Input the diffraction spots into the error backpropagation module of the feedforward neural network to calculate the deviation amount between the actual phase distribution and the target Bloch mode; Generate wavefront correction parameters in the form of Zernike polynomial coefficients based on the deviation amount.

[0010] Furthermore, the dynamic closed-loop calibration mechanism includes: Input the Zernike polynomial coefficients into the input layer of the feedforward neural network to form a first feedback loop; Dynamically weight and correct the eigenvalues of the transfer function matrix through a Kalman filter to form a second feedback loop; The outputs of the first feedback loop and the second feedback loop are convolved and fused in the Fourier spectrum domain of the waveguide mode.

[0011] Further, the discretized substrate optical field synthesis method includes: Construct a discretization constraint condition for the Bloch wave vector according to the reciprocal lattice vector space distribution of the photonic crystal waveguide; Project the continuous phase distribution of the refractive index gradient field onto the basis vectors of the reciprocal lattice vector space; Screen the discretized phase components that satisfy the group velocity matching condition of the Bloch mode through the Gibbs sampling algorithm.

[0012] Further, the generation of the N - order controllable diffracted optical field includes: Set a 4f optical filtering system at the output end of the photonic crystal waveguide; Insert a spiral phase plate corresponding to the target topological charge number in the Fourier plane of the 4f optical filtering system; Suppress the diffraction efficiency of non - target order Bloch modes through the mode field matching effect of the graded refractive index cladding.

[0013] A high - precision light column display system based on liquid crystal variable refractive index, the system includes: A refractive gradient regulation model, which generates a multi - dimensional driving signal with spatial gradient characteristics according to the preset spatial distribution parameters of the target light column. Through the coupling regulation of the voltage amplitude and frequency of the multi - dimensional driving signal, the molecular arrangement state of the liquid crystal electro - optic refractive index adjustment layer is dynamically changed, and a refractive index gradient field matching the phase distribution requirement along the light column axis is established; A waveguide substrate generation model, which couples the incident light beam into the total internal reflection transmission channel of the optical waveguide structure, performs spatial phase modulation on the transmitted light beam based on the refractive index gradient field, and generates a discretized substrate optical field adapted to the geometric constraint conditions of the optical waveguide structure through the geometric boundary constraint effect of the optical waveguide structure; A polarization diffraction synthesis model, which applies synchronous polarization state regulation to the discretized substrate optical field, dynamically corrects the polarization dispersion angle deviation of each diffraction order by using a birefringence compensation algorithm, and generates an N - order controllable diffracted optical field with a fixed phase relationship through multi - level diffraction synthesis; Closed-loop dynamic reconstruction model. The closed-loop dynamic reconstruction model imports the Nth-order controllable diffracted light field into the free-space propagation domain, realizes the spatial superposition of diffracted fields of each order through Fresnel diffraction integral, reconstructs a continuous and high-precision light column shape, and uses the wavefront distortion amount feedback detected by the light column edge to inversely correct the voltage regulation parameters of the driving signal to form a dynamic closed-loop calibration mechanism.

[0014] Technical effects and advantages of the high-precision light column display method and system based on liquid crystal variable refractive index provided by the present invention: Through the discretized cooperative mapping mechanism of waveguide mode-phase field and the dual-loop dynamic anti-interference architecture, the present invention realizes the real-time generation of high-resolution light columns and stable transmission in complex environments without mechanical scanning components, combining high precision and strong robustness. The present invention integrates the reciprocal lattice vector constraint characteristics of photonic crystal waveguides into the generation of driving signals. Through the discretized substrate light field synthesis algorithm, the continuous refractive index gradient field is mapped into a phase distribution compatible with the waveguide eigenmode, fundamentally eliminating the light field breakage problem caused by mode mismatch, and significantly improving the spatial consistency of the light column shape; constructing a dual-loop collaboration enables the light column to maintain sub-wavelength edge sharpness under complex interference; combining the joint regulation of the 4f optical system and the spiral phase plate, and screening the optimal discrete phase components through the Gibbs sampling algorithm, greatly improving the light field energy ratio of the target diffraction order and effectively suppressing stray light interference, realizing the efficient directional transmission of light column energy; constructing a non-linear driving model based on a feed-forward neural network to dynamically analyze the complex mapping relationship between waveguide modes and driving signals, and adapting to different medium environments (such as air, liquid, flexible substrate) without hardware reconstruction. Brief Description of the Drawings

[0015] Figure 1 It is a flowchart of the high-precision light column display method based on liquid crystal variable refractive index in Embodiment 1; Figure 2 It is a schematic connection diagram of the high-precision light column display system based on liquid crystal variable refractive index in Embodiment 2. Detailed Embodiments

[0016] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0017] Embodiment 1: Please refer to Figure 1 As shown, the embodiment of the present invention provides a high-precision light column display method based on liquid crystal variable refractive index. The method includes: According to the preset spatial distribution parameters of the target light column, a multi-dimensional driving signal with spatial gradient characteristics is generated. Through the coupled regulation of the voltage amplitude and frequency of the multi-dimensional driving signal, the molecular arrangement state of the liquid crystal electro-optic refractive index adjustment layer is dynamically changed, and a refractive index gradient field matching the axial phase distribution requirement of the light column is established.

[0018] Couple the incident light beam into the total reflection transmission channel of the optical waveguide structure, perform spatial phase modulation on the transmitted light beam based on the refractive index gradient field, and generate a discretized base light field adapted to the geometric constraint conditions of the optical waveguide structure through the geometric boundary constraint effect of the optical waveguide structure.

[0019] Apply polarization state synchronous regulation to the discretized base light field, dynamically correct the polarization dispersion angle deviation of each diffraction order using the birefringence compensation algorithm, and generate an N-order controllable diffraction light field with a fixed phase relationship through multi-level diffraction synthesis.

[0020] Introduce the N-order controllable diffraction light field into the free space propagation domain, realize the spatial superposition of each order diffraction field through the Fresnel diffraction integral, reconstruct a continuous and high-precision light column shape, and use the wavefront distortion amount detected and fed back at the light column edge to inversely correct the voltage regulation parameters of the driving signal, forming a dynamic closed-loop calibration mechanism.

[0021] The method for generating the multi-dimensional driving signal includes: According to the Bloch mode eigen-equation of the optical waveguide structure, establish a transfer function matrix between the driving voltage and the phase modulation.

[0022] The Bloch mode eigen-equation is used to describe the propagation characteristics of electromagnetic waves in a periodic optical waveguide. Its eigen-solutions correspond to the guided mode forms supported by the optical waveguide. By substituting the dielectric constant distribution parameters of the liquid crystal electro-optic refractive index adjustment layer into the equation, a transfer function matrix between the driving voltage and the phase modulation is constructed. The transfer function matrix quantitatively characterizes the mapping relationship between the voltage amplitude and frequency combination applied to the traveling wave electrodes and the molecular arrangement state of the liquid crystal molecules, and its dimension is determined by the number of electrode units that can be independently regulated in the optical waveguide.

[0023] Perform an inverse operation on the transfer function matrix through a feedforward neural network to generate a pre-distorted driving signal including inter-mode coupling compensation.

[0024] To realize the inverse operation of the transfer function matrix, a feedforward neural network is used for non-linear approximation; the input layer of the neural network is the theoretical voltage vector calculated according to the target phase distribution, the hidden layer includes multiple layers of non-linear activation nodes to simulate the inter-mode coupling effect, and the output layer generates the driving signal parameters including pre-distortion compensation.

[0025] Exemplarily: When the target phase gradient requires a phase difference of π / 4 between adjacent electrode units in the optical waveguide, the neural network will predict the reverse coupling compensation amount to be superimposed based on historical training data, generate a pre-distorted voltage sequence capable of canceling mode crosstalk. During the training process, by comparing the error between the actual phase modulation result and the theoretical value, the network weight parameters are continuously optimized, and finally the pre-distortion accuracy of the driving signal reaches the sub-wavelength level.

[0026] Load the pre-distorted driving signal onto the traveling-wave electrode of the electro-optic modulator to form a refractive index gradient field with spatio-temporal distribution.

[0027] When loading the pre-distorted driving signal output by the neural network onto the traveling-wave electrode of the optical waveguide structure, the spatio-temporal synchronization of electromagnetic wave propagation needs to be considered. The traveling-wave electrode adopts a distributed capacitive coupling design, and its electrical signal propagation speed matches the group velocity of the light beam in the optical waveguide.

[0028] Exemplarily: When the driving frequency is set to 10 kHz, the voltage amplitude of the traveling-wave electrode can be dynamically adjusted in the range of 0 V to 5 V. By controlling the voltage gradient direction and amplitude change rate of adjacent electrode units, a refractive index gradient field with a specific spatial frequency can be formed in the liquid crystal layer. The spatial distribution characteristics of the refractive index gradient field are strictly matched with the axial phase requirements of the light column, thereby ensuring the discretization accuracy of the base light field during the subsequent light field modulation process. During this process, the parasitic capacitance effect between the electrodes has been pre-compensated by the pre-distortion algorithm to avoid the refractive index distribution distortion caused by signal delay.

[0029] The above multi-dimensional driving signal generation method effectively solves the problem of phase modulation non-linearity caused by mode coupling in traditional open-loop driving by introducing a pre-distortion mechanism driven by a neural network. The refractive index gradient field generated by the multi-dimensional driving signal generation method can reach the physical limit of the optical waveguide periodic structure in terms of transverse resolution, and the broadening range of the gradient transition region is controlled within 20% of the size of a single electrode unit, laying a foundation for the precise synthesis of the subsequent discretized base light field.

[0030] The optical waveguide structure is a photonic crystal waveguide, including: A hexagonal close-packed air hole array arranged periodically along the propagation direction, and the duty cycle of the air holes matches the group velocity distribution of the Bloch mode.

[0031] The construction process of the photonic crystal waveguide needs to meet the dual requirements of Bloch mode and group velocity regulation. The ratio of the air hole period to the lattice constant (i.e., the duty cycle) is optimized by photonic bandgap engineering. In the design, the selection of the air hole duty cycle needs to match the eigenfield distribution of the Bloch mode at the target working wavelength.

[0032] Exemplarily: When operating in the visible light band, the duty cycle is adjusted so that the cutoff frequency of the photonic band gap overlaps with the guided mode group velocity range required for the light column display, thereby ensuring that the light beam propagates inside the waveguide with quasi-linear group velocity dispersion characteristics.

[0033] This design ensures that when the driving signal induces a refractive index gradient field in the liquid crystal, the spatial distribution of the wave vector of the light beam can quickly respond to the change in refractive index and maintain the continuity of the wavefront during the phase modulation process.

[0034] The refractive index of the gradient refractive index cladding covering the side wall of the waveguide is distributed in a hyperbolic secant function along the radial direction, and is used to constrain the paraxial propagation characteristics of the refractive index gradient field.

[0035] The gradient refractive index cladding set on the side wall of the waveguide adopts the refractive index control strategy of hyperbolic secant function distribution. The material of the gradient refractive index cladding is composed of a polymer doped with nanoparticles with a concentration gradient distribution. Its refractive index increases from the waveguide core interface to the outside along the diameter. Press The law of decreasing, among which is the core layer refractive index reference value, is the attenuation coefficient; this distribution characteristic can be equivalent to a lens-like focusing effect, so that in the process of establishing the refractive index gradient field, the light field component transmitted along the axis is suppressed by the exponential decay type loss.

[0036] Exemplary: When the refractive index gradient field established in the liquid crystal layer causes the light beam to deflect laterally, the energy of the paraxial component will be confined to the effective mode field diameter of the waveguide by the gradient refractive index barrier in the cladding, preventing the distortion of the substrate light field caused by leakage of high-order modes.

[0037] In the specific implementation, the duty cycle of the air hole array and the cladding attenuation coefficient need to be collaboratively optimized through joint simulation; by solving the eigenvalue solution of Maxwell's equations by the finite element method, it can be observed that when the air hole duty cycle is in a specific range, the Bloch mode supported by the waveguide reaches a balance between the lateral confinement ability and the group velocity control sensitivity; at this time, the potential well depth formed by the cladding refractive index gradient can just compensate for the mode coupling disturbance caused by the liquid crystal refractive index gradient field, so that the phase distribution of the transmitted light beam is always synchronized with the axial phase requirement of the target light column; this synergistic effect ensures that even in the process of high-order diffraction synthesis, the spatial frequency components of the discretized substrate light field can still strictly meet the geometric constraints of the optical waveguide structure, avoiding the decrease in diffraction efficiency due to mode mismatch.

[0038] Through the design of the above optical waveguide structure, the photonic crystal waveguide realizes the shaping and screening of the spatial spectrum of the substrate optical field. When the incident light beam is coupled into the waveguide, its high-order spatial frequency components are filtered out by the bandgap effect of the air hole array, while the fundamental mode components maintain stable transmission characteristics under the constraint of the tapered cladding. This spectrum shaping effect and the pre-distorted driving signal form a spatial-spectrum complementary mechanism, jointly ensuring the linearity and dynamic range of the refractive index gradient field for the phase modulation of the transmitted light beam, and providing a high-fidelity physical carrier for subsequent multi-stage diffraction synthesis.

[0039] The polarization state synchronous control method includes: Integrate a polarization beam splitter at the input end of the photonic crystal waveguide to decompose the incident light into orthogonal polarization components of TE mode and TM mode.

[0040] Integrate a cascaded polarization beam splitter at the waveguide input end. This device is composed of a birefringent crystal prism and a phase compensation layer, and can decompose the incident light into two orthogonal polarization components of TE mode (transverse electric mode) and TM mode (transverse magnetic mode); during the decomposition process, utilize the sensitivity of the hexagonal close-packed air hole array in the photonic crystal waveguide to the polarization state, and by adjusting the prism cutting angle, align the electric field vector of the TE mode with the main axis of the air hole array, while the magnetic field component of the TM mode forms a strong coupling with the tapered refractive index cladding of the waveguide sidewall, so that the two polarization components occupy different equivalent refractive index channels in the waveguide, laying a physical foundation for subsequent independent control.

[0041] Apply the odd and even channel voltages in the pre-distorted driving signal to the TE mode and TM mode respectively.

[0042] Since the group velocity dispersion of the TE mode is significantly affected by the air hole duty cycle, and the mode field distribution of the TM mode is more sensitive to the cladding refractive index gradient, the pre-distorted signal generated by the neural network needs to perform feature decoupling for different polarization states.

[0043] Exemplarily: When processing the TE mode, the driving voltage applied to the odd-numbered electrode columns needs to focus on compensating for the mode coupling distortion caused by the air hole array; while the voltage of the even-numbered columns corresponding to the TM mode focuses on suppressing the paraxial phase drift brought by the tapered cladding; this polarization separation strategy for odd and even channels enables the pre-distortion algorithm to perform directional correction for the optical field distortion mechanisms of different polarization states.

[0044] Through the time-domain interleaved scanning method, make the birefringent delay of the orthogonal polarization components form a complementary distribution in space.

[0045] Divide each refresh period into multiple time windows, and preferentially drive the odd-numbered electrode columns corresponding to the TE mode in odd-numbered windows, while activate the even-numbered electrode columns of the TM mode in even-numbered windows.

[0046] Exemplarily: During a scanning period with a duration of τ, in the first 0.5τ period, the refractive index gradient required to establish the TE mode is formed in the liquid crystal layer through the voltages of odd-numbered columns, and in the subsequent 0.5τ period, the voltages are switched to the even-numbered columns to regulate the phase distribution of the TM mode. Since the response time of the liquid crystal material is much smaller than τ, the birefringence delay effects of the two polarization components will form an alternately complementary phase grating in space, and polarization state fusion is achieved on the observation plane through the persistence of vision effect.

[0047] When the TE mode generates a phase delay of π / 2 under the drive of odd-numbered columns, the TM mode obtains a delay of -π / 2 through compensation by even-numbered columns. After their spatial superposition, a complete π-phase difference closed loop is formed. This complementary mechanism not only cancels out the polarization-dependent losses inherent in the waveguide structure but also suppresses the polarization crosstalk noise below the background noise level through the time-averaging effect.

[0048] Through the above-mentioned synchronous regulation of polarization states, the regulation dimension of the pre-distorted drive signal is effectively extended to the polarization domain, and at the same time, it can form an organic cooperation with the characteristics of the waveguide structure. The hexagonal symmetry of the air hole array provides a geometric constraint for the separation of the TE mode and the TM mode, while the mode field screening effect of the tapered cladding ensures the mode purity of each polarization component during the regulation process. This multi-physical field coupling design enables the high-precision light column display system to break through the crosstalk bottleneck of traditional polarization multiplexing technology and provide a high-contrast physical light field substrate for dynamic holographic imaging.

[0049] The detection methods for wavefront distortion amounts include: Collect the diffraction spots of orthogonal polarization components at the output end of the polarization beam splitter.

[0050] Exemplarily: When the mode field diameter of the TE mode at the output end face of the waveguide is 10 μm, the magnification of the objective lens is set to 40 times, so that a single pixel can resolve a wavefront phase gradient change of 0.25 μm. The collected diffraction spots are transmitted to a high-speed image sensor through a polarization-maintaining optical fiber to form an interference fringe pattern containing spatial phase information.

[0051] Input the diffraction spots into the error backpropagation module of the feedforward neural network to calculate the deviation between the actual phase distribution and the target Bloch mode.

[0052] First, extract the complex amplitude distribution of the spots through Fourier transform, decompose it into an amplitude term and a phase term. After the phase term is processed by the phase unwrapping algorithm, it is compared pixel by pixel with the ideal phase distribution of the target Bloch mode.

[0053] Exemplarily: When the target mode requires the output end face of the waveguide to form a spiral phase distribution, the neural network will perform a convolution operation on the actually measured phase gradient and the theoretical helicity to generate an error matrix containing the aberration spatial frequency characteristics. This error matrix updates the network weights through the backpropagation path, enabling the subsequent generated predistortion drive signal to automatically compensate for the cumulative phase error.

[0054] Generate wavefront correction parameters in the form of Zernike polynomial coefficients based on the deviation.

[0055] The mapping process from the error matrix to the Zernike polynomial coefficients uses the mode orthogonal decomposition method, and the mode orthogonal decomposition method includes: Project the phase deviation onto the basis function space of 36-term Zernike polynomials, and obtain the coefficient weights of each order by least squares fitting.

[0056] Exemplarily: When the coefficient of the defocus term (Z4) in the measured wavefront is 0.15λ, it indicates the existence of axial non-uniformity in the refractive index gradient field of the liquid crystal layer, and the voltage gradient slope of the drive signal needs to be adjusted; if the coefficients of the astigmatism terms (Z5 / Z6) exceed the threshold, it reflects the misalignment of the polarization beam splitter, and a mechanical fine-tuning mechanism needs to be triggered for compensation.

[0057] The effectiveness of the wavefront distortion detection method stems from the physical correspondence between Zernike polynomials and optical system aberrations. When the refractive index gradient field of the liquid crystal layer undergoes thermally induced deformation due to environmental temperature fluctuations, the resulting wavefront distortion is mainly manifested as low-order aberrations (such as coma and trefoil aberration). By real-time monitoring the change trend of the Zernike coefficient vector, the system mismatch direction can be predicted in advance and a compensation amount can be injected. For example, when it is detected that the coefficient of Z7 (vertical coma) continues to increase, the neural network will automatically superimpose a reverse tilt phase on the odd-column drive signal to cancel the phase nonlinearity caused by material thermal expansion through the predistortion algorithm.

[0058] Through the above wavefront distortion detection method, the training dataset of the neural network can also be dynamically expanded. The Zernike coefficients and the corresponding drive signal adjustment amounts generated in each wavefront correction process are recorded as new training samples, enabling the network to gradually master the non-linear mapping relationship between environmental disturbances and system responses. This self-learning ability enables the light column display system to still provide guarantees for the stable synthesis of multi-level diffraction light fields in the face of disturbances such as mechanical vibration and temperature drift, and at the same time form a synergistic effect with polarization spatio-temporal control, that is, the Zernike coefficients not only correct the overall wavefront distortion, but also separately optimize the polarization state consistency of the TE / TM modes through the odd-even term separation mechanism, and finally achieve the output of a light field with controllable full Stokes parameters.

[0059] The dynamic closed-loop calibration mechanism includes: Input the Zernike polynomial coefficients into the input layer of the feedforward neural network to form the first feedback loop.

[0060] Dynamically weight and correct the eigenvalues of the transfer function matrix through a Kalman filter to form the second feedback loop.

[0061] In a photonic crystal waveguide, the eigenvectors of the transfer function matrix correspond to the field distribution patterns of Bloch modes, while the eigenvalues characterize the mode attenuation rate and the phase accumulation speed; and the Kalman filter can, through a recursive prediction-correction algorithm, real-time estimate the eigenvalue drift caused by environmental perturbations; for example, when the temperature rises resulting in a decrease in the refractive index of the waveguide core layer, the filter will predict the real part change rate of the TE mode eigenvalue based on historical observation data and apply a negative feedback weight to suppress its deviation from the set value.

[0062] The outputs of the first feedback loop and the second feedback loop are convolutionally fused in the Fourier spectrum domain of the waveguide mode.

[0063] Perform a two-dimensional Fourier transform on the drive signal correction amount output by the first feedback loop to obtain its spectral amplitude-phase distribution; at the same time, map the eigenvalue correction parameters of the second feedback loop to the frequency-domain transfer coefficients of the transfer function; the first feedback loop and the second feedback loop perform a complex convolution operation in the spatial frequency domain to achieve the collaborative optimization of low-frequency phase error correction and high-frequency noise suppression.

[0064] The core advantage of the dynamic closed-loop calibration mechanism lies in the time constant complementarity of the dual loops. The first feedback loop, based on the fast inference ability of the neural network (microsecond-level response), mainly compensates for the deterministic distortion caused by the nonlinearity of the drive signal; the second feedback loop, relying on the state prediction characteristics of the Kalman filter (millisecond-level update), focuses on suppressing the random errors brought about by the drift of environmental parameters. The two achieve dynamic balance through the weight allocation of the Fourier-domain convolution kernel, giving higher weight to the first loop at the startup stage for rapid convergence, and increasing the contribution of the second loop during the steady-state operation to maintain long-term stability.

[0065] The discrete basis optical field synthesis method includes: According to the reciprocal lattice vector space distribution of the photonic crystal waveguide, construct the discretization constraint conditions of the Bloch wave vector; the construction method includes: First, based on the periodic structure of the hexagonal lattice air hole array, construct a three-dimensional coordinate system in the reciprocal lattice vector space, and then determine the allowable Bloch wave vector discretization in the reciprocal lattice vector space by calculating the Fourier transform of the waveguide lattice basis vectors. For example, when the waveguide lattice constant is 5μm, the reciprocal lattice vector basis vector spacing is 2π / (3μm), forming discrete wave vector nodes with a hexagonal distribution.

[0066] Project the continuous phase distribution of the refractive index gradient field onto the basis vectors of the reciprocal lattice vector space. The projection method uses the mode orthogonal decomposition technique, which includes treating the continuous phase surface generated by the liquid crystal layer as a metasurface, and performing a dot product operation between the phase gradient of each pixel point and the reciprocal lattice basis vectors to obtain the weight coefficients of the corresponding discrete wave vector components. For example, when the phase gradient direction in a certain region forms a 30° angle with the reciprocal lattice basis vector G1, this gradient will be decomposed into the projection components of G1 and its adjacent basis vectors G2 and G3, forming a discretized wave vector combination.

[0067] Use the Gibbs sampling algorithm to screen the discretized phase components that satisfy the Bloch mode group velocity matching condition; when the group velocity angle between two wave vector components k1 and k2 exceeds the waveguide mode coupling threshold, their joint probability weight decays according to the exponential law. During the sampling process, the possible component combinations are traversed through the Markov chain Monte Carlo method, and gradually converge to the lowest energy state.

[0068] The physical essence of the discretized base light field synthesis method lies in reconstructing the continuous light field using the discrete transmission characteristics of the waveguide. The reciprocal lattice vector projection transforms the traditional continuous phase modulation into an eigenmode excitation problem, fundamentally avoiding the energy loss outside the waveguide cut-off frequency. The statistical optimization mechanism introduced by Gibbs sampling effectively solves the problem of group velocity mismatch caused by multimode coupling.

[0069] At the same time, the eigenvalues of the transfer function corrected by the Kalman filter provide real-time parameter updates for the energy function of Gibbs sampling; the Zernike coefficient feedback of the discretized base light field in turn optimizes the weight distribution of the reciprocal lattice vector projection, so as to be able to adaptively adjust the spatial distribution density of the discrete components; the finally formed discretized base light field provides an optimization space with clear physical constraints for the neural network to generate high-fidelity predistortion signals.

[0070] In the Nth-order controllable diffracted light field, N is a preset value. The generation of the Nth-order controllable diffracted light field includes: Set a 4f optical filtering system at the output end of the photonic crystal waveguide.

[0071] Insert a spiral phase plate corresponding to the target topological charge number in the Fourier plane of the 4f optical filtering system.

[0072] Through the mode field matching effect of the graded refractive index cladding, suppress the diffraction efficiency of non-target order Bloch modes.

[0073] When the discrete base light field and the 4f spectral filtering act jointly, the former constrains the physical realizability of spatial frequency components through reciprocal lattice vector projection, and the latter uses spiral phase modulation to screen the eigenmodes that conform to the target angular momentum state. The graded-index cladding, as a spatial filter, further suppresses the stray modes excited by waveguide defects or environmental perturbations, laying a physical foundation for the light column display system to achieve dynamic holographic projection with sub-wavelength accuracy.

[0074] Embodiment 2: As Figure 2 shown, based on the same inventive concept as the high-precision light column display method based on liquid crystal variable refractive index in the foregoing embodiment, the present application provides a high-precision light column display system based on liquid crystal variable refractive index. The system in the embodiment of the present application and the method embodiment are based on the same inventive concept. Among them, the system includes: A refractive gradient regulation model, which generates a multi-dimensional drive signal with spatial gradient characteristics according to the preset spatial distribution parameters of the target light column. By coupling and regulating the voltage amplitude and frequency of the multi-dimensional drive signal, the molecular arrangement state of the liquid crystal electro-optic refractive index adjustment layer is dynamically changed, and a refractive index gradient field matching the requirements of the axial phase distribution of the light column is established.

[0075] A waveguide substrate generation model, which couples the incident light beam into the total internal reflection transmission channel of the optical waveguide structure, performs spatial phase modulation on the transmitted light beam based on the refractive index gradient field, and generates a discretized base light field adapted to the geometric constraint conditions of the optical waveguide structure through the geometric boundary constraint effect of the optical waveguide structure.

[0076] A polarization diffraction synthesis model, which applies synchronous polarization state regulation to the discretized base light field, dynamically corrects the polarization dispersion angle deviation of each diffraction order by using the birefringence compensation algorithm, and generates an N-order controllable diffraction light field with a fixed phase relationship through multi-stage diffraction synthesis.

[0077] A closed-loop dynamic reconstruction model, which introduces the N-order controllable diffraction light field into the free space propagation domain, realizes the spatial superposition of each order diffraction field through the Fresnel diffraction integral, reconstructs a continuous high-precision light column shape, and uses the wavefront distortion amount detected and fed back at the light column edge to inversely correct the voltage regulation parameters of the drive signal, forming a dynamic closed-loop calibration mechanism.

[0078] Obviously, those skilled in the art can make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalent technologies, the present invention is also intended to include these changes and modifications.

[0079] The above are only the preferred specific embodiments of the present application, but the protection scope of the present application is not limited thereto. Any person skilled in the art within the technical scope disclosed by the present application should cover within the protection scope of the present application any equivalent replacement or change made according to the technical solution and its concept of the present application.

Claims

1. A high-precision light column display method based on liquid crystal variable refractive index, characterized in that The method includes: Generating a multi-dimensional driving signal with spatial gradient characteristics according to the preset spatial distribution parameters of the target light column, and dynamically changing the molecular arrangement state of the liquid crystal electro-optic refractive index adjustment layer through the coupling regulation of the voltage amplitude and frequency of the multi-dimensional driving signal, so as to establish a refractive index gradient field matching the axial phase distribution requirement of the light column; Coupling the incident light beam into the total reflection transmission channel of the optical waveguide structure, performing spatial phase modulation on the transmitted light beam based on the refractive index gradient field, and generating a discretized base light field adapted to the geometric constraint conditions of the optical waveguide through the geometric boundary constraint effect of the optical waveguide structure; Applying polarization state synchronous regulation to the discretized base light field, dynamically correcting the polarization dispersion angle deviation of each diffraction order by using the birefringence compensation algorithm, and generating an N-order controllable diffraction light field with a fixed phase relationship through multi-stage diffraction synthesis; Introducing the N-order controllable diffraction light field into the free space propagation domain, realizing the spatial superposition of each order diffraction field through the Fresnel diffraction integral, reconstructing a continuous and high-precision light column shape, and using the wavefront distortion amount detected by the light column edge detection to inversely correct the voltage regulation parameters of the driving signal to form a dynamic closed-loop calibration mechanism.

2. The high-precision light column display method based on liquid crystal variable refractive index according to claim 1, characterized in that The multi-dimensional driving signal generation method includes: Establishing a transfer function matrix of the driving voltage and phase modulation according to the Bloch mode eigen-equation of the optical waveguide structure; Performing an inverse operation on the transfer function matrix through a feed-forward neural network to generate a pre-distorted driving signal including inter-mode coupling compensation; Loading the pre-distorted driving signal onto the traveling wave electrode of the electro-optic modulator to form a refractive index gradient field with spatio-temporal distribution.

3. The high-precision light column display method based on liquid crystal variable refractive index according to claim 2, wherein The optical waveguide structure is a photonic crystal waveguide, and the optical waveguide structure includes: A hexagonal close-packed air hole array arranged periodically along the propagation direction, and the duty cycle of the air holes matches the group velocity distribution of the Bloch mode; A graded refractive index cladding covering the waveguide sidewall, and its refractive index is distributed in a hyperbolic secant function along the radial direction, which is used to constrain the paraxial propagation characteristics of the refractive index gradient field.

4. The high-precision light column display method based on liquid crystal variable refractive index according to claim 3, characterized in that The polarization state synchronous regulation method includes: Integrating a polarization beam splitter at the input end of the photonic crystal waveguide to decompose the incident light into TE mode and TM mode orthogonal polarization components; Applying the odd and even channel voltages in the pre-distorted driving signal to the TE mode and TM mode respectively; Through the time-domain interleaved scanning method, the birefringence delay amounts of the orthogonal polarization components form a complementary distribution in space.

5. The high-precision light column display method based on liquid crystal variable refractive index according to claim 4, wherein, The wavefront distortion amount detection method includes: Collecting the diffraction spots of the orthogonal polarization components by using the output end of the polarization beam splitter; Inputting the diffraction spots into the error backpropagation module of the feed-forward neural network to calculate the deviation amount between the actual phase distribution and the target Bloch mode; Generating wavefront correction parameters in the form of Zernike polynomial coefficients based on the deviation amount.

6. The high-precision light column display method based on liquid crystal variable refractive index according to claim 5, characterized in that, The dynamic closed-loop calibration mechanism includes: Inputting the Zernike polynomial coefficients into the input layer of the feed-forward neural network to form a first feedback loop; Dynamically weighting and correcting the eigenvalues of the transfer function matrix through a Kalman filter to form a second feedback loop; The outputs of the first feedback loop and the second feedback loop are convolutionally fused in the Fourier spectral domain of the waveguide mode.

7. The high-precision light column display method based on liquid crystal variable refractive index according to claim 4, characterized in that, The discrete base optical field synthesis method includes: Constructing a discretization constraint condition for the Bloch wave vector according to the reciprocal lattice vector spatial distribution of the photonic crystal waveguide; Projecting the continuous phase distribution of the refractive index gradient field onto the basis vectors of the reciprocal lattice vector space; Screening discrete phase components that satisfy the group velocity matching condition of the Bloch mode through the Gibbs sampling algorithm.

8. The high-precision light column display method based on liquid crystal variable refractive index according to claim 7, characterized in that The generation of the Nth-order controllable diffracted optical field includes: Setting up a 4f optical filtering system at the output end of the photonic crystal waveguide; Inserting a spiral phase plate corresponding to the target topological charge number in the Fourier plane of the 4f optical filtering system; Suppressing the diffraction efficiency of non-target order Bloch modes through the mode field matching effect of the graded refractive index cladding.

9. A high-precision light column display system based on a liquid crystal variable refractive index, characterized in that The system includes: A refractive gradient regulation model, which generates a multi-dimensional driving signal with spatial gradient characteristics according to the preset spatial distribution parameters of the target light column. Through the coupled regulation of the voltage amplitude and frequency of the multi-dimensional driving signal, the molecular arrangement state of the liquid crystal electro-optic refractive index adjustment layer is dynamically changed, and a refractive index gradient field matching the axial phase distribution requirement of the light column is established; A waveguide substrate generation model, which couples the incident light beam into the total reflection transmission channel of the optical waveguide structure, performs spatial phase modulation on the transmitted light beam based on the refractive index gradient field, and generates a discretized base optical field adapted to the geometric constraint conditions of the optical waveguide structure through the geometric boundary constraint effect of the optical waveguide structure; A polarization diffraction synthesis model, which applies synchronous polarization state regulation to the discretized base optical field, dynamically corrects the polarization dispersion angle deviation of each diffraction order by using the birefringence compensation algorithm, and generates an Nth-order controllable diffracted optical field with a fixed phase relationship through multi-stage diffraction synthesis; A closed-loop dynamic reconstruction model, which introduces the Nth-order controllable diffracted optical field into the free space propagation domain, realizes the spatial superposition of each order diffracted field through the Fresnel diffraction integral, reconstructs a continuous and high-precision light column shape, and uses the wavefront distortion amount detected and fed back at the light column edge to reversely correct the voltage regulation parameters of the driving signal to form a dynamic closed-loop calibration mechanism.

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