A method for generating an initial structure for a hybrid folded super-zoom optical system

Abstract

This invention relates to a method for generating the initial structure of a hybrid cascaded metasurface zoom optical system, belonging to the fields of optical design and metasurface imaging technology. This method targets zoom systems composed of a propagation space, a cascaded zoom metasurface, and multiple fixed refractive lenses. It employs paraxial tracing, differential evolution, multi-focal-length nonlinear root finding, and third-order aberration linearization to jointly determine the axial positions of each optical surface, the fixed refractive power, and the equivalent optical power trajectory of the cascaded metasurface across focal lengths. Furthermore, it inversely obtains the geometry of the refractive lenses and the mechanical motion trajectory and phase design target of the cascaded metasurface. This enables rapid generation of the initial structure for multi-focal-length continuous zoom under fixed total length and fixed image plane conditions, and is suitable for the design of miniaturized zoom imaging systems.

Description

Technical Field

[0001] This invention relates to the fields of initial structure design of zoom optical systems, metasurface optics, and hybrid imaging optics design, and specifically to an initial structure design method for a hybrid super zoom optical system.

[0002] The term "hybrid refractive superzoom optical system" as used in this specification refers to a zoom imaging system composed of fixed refractive optical units and variable metasurface optical units. The system can employ a linear optical path, or, in engineering implementation, may include folded propagation sections. This invention focuses on a unified modeling and solution method for this type of system in the initial structural stage. Background Technology

[0003] Zoom optical systems are a core component of modern imaging devices, achieving clear imaging of targets at different distances by adjusting the system's focal length. With the increasing demands for miniaturization and lightweight imaging systems in applications such as UAV payloads, mobile terminals, and medical endoscopes, traditional refractive or catadioptric zoom systems, due to their multiple movable mirror groups that can move along the optical axis, suffer from complex structures and large volumes, making them unsuitable for the engineering constraints of these applications. Existing initial structure design methods for zoom systems typically obtain the initial system structure through paraxial quantity allocation, aberration balancing, and multi-state simultaneous solutions, using this as a starting point for subsequent precise optical optimization. However, when metasurface optical elements are introduced into the system, the aforementioned traditional methods struggle to simultaneously handle the strong coupling relationship between traditional optical components and metasurface optical elements within a unified solution framework, thus failing to provide a physically feasible initial structure for hybrid zoom systems containing metasurfaces.

[0004] Metasurfaces are planar optical devices composed of periodic or aperiodic arrangements of subwavelength structural units. They enable independent and precise control of the amplitude, phase, and polarization of transmitted or reflected light fields within extremely thin device thicknesses, offering significant advantages such as light weight, small thickness, and ease of integration. Cascaded metasurface structures, through the coordinated operation of two or more metasurface devices, utilize relative lateral displacement to achieve continuous modulation of the emitted wavefront, thus enabling continuous zoom functionality without the need for axial motion mechanisms. This provides a new technological path for the realization of miniaturized imaging systems. The hybrid superzoom optical system uses fixed refractive or catadioptric units to handle wide field-of-view imaging and principal focal length support, while cascaded metasurface units handle rapid and precise wavefront modulation and continuous zoom. The two have a clear division of labor and complement each other, which can not only significantly reduce the structural complexity of traditional continuous zoom systems caused by multiple moving lens groups, but also utilize the high wavefront control freedom of metasurfaces to simultaneously achieve zoom and partial aberration correction in a small axial space. The fixed refractive units complement the metasurfaces in aberration, synergistically improving the overall imaging quality. Its comprehensive performance is superior to that of pure metasurface optical systems.

[0005] Current research on the application of metasurfaces in zoom imaging systems mainly focuses on improving local performance, such as phase profile design of individual metasurface devices, selection of micro / nano structure units, and optimization of driving methods. A method for generating the initial structure of the entire hybrid superzoom system is lacking. Specifically, existing methods cannot further unify the system-level focal length variation schedule, fixed image plane constraints, and overall aberration distribution results into refractive unit structural parameters, optical power trajectories of cascaded metasurface states, and metasurface phase distribution targets. This restricts the entire process of such systems moving from conceptual design to engineering implementation. Therefore, a method for generating the initial structure of hybrid superzoom optical systems is urgently needed to achieve joint modeling and global solution of refractive units and cascaded metasurface units, and to provide a physically feasible initial structure for subsequent accurate optimization, device design, and engineering implementation. Summary of the Invention

[0006] The purpose of this invention is to overcome the problem that existing hybrid zoom systems lack design experience to draw upon in their initial structural design and are difficult to obtain an initial structure that can be further optimized by optical design software.

[0007] To address the aforementioned issues, this invention provides an initial structure generation method for hybrid superzoom optical systems. This method is used to jointly determine the system's axial layout, fixed optical unit parameters, state optical power trajectory of the zoom metasurface group, and phase distribution design under constraints of limited system total length, fixed image plane, and multi-focal-length continuous zoom.

[0008] To achieve the above objectives, the present invention adopts the following technical solution:

[0009] A method for generating the initial structure of a hybrid refractive superzoom optical system, the hybrid refractive superzoom optical system comprising at least one folded propagation section, at least one fixed optical unit, and at least one cascaded metasurface zoom unit; the fixed optical unit is preferably a fixed refractive optical unit, and the cascaded metasurface zoom unit is composed of two metasurface phase plates capable of relative mechanical motion to generate changes in optical power; the method includes the following steps:

[0010] Step 1: Establish a design schedule and candidate topologies.

[0011] Step 1-1, let the total length of the system be... The fixed image plane position is The target focal length sequence is The full field of view sequence corresponding to the focal length of each target is as follows: Where L represents the number of target focal length states. When the input is the full field of view, it is converted to a half field of view: ,in, This represents the half field of view angle corresponding to the focal length state of the j-th target.

[0012] Steps 1-2: Based on this, establish a set of candidate topologies. For each candidate topology, set an initial range and a family of positive and negative signs for the optical power of the fixed refractive optical unit.

[0013] Step 2: Parametrically configure the axial layout and fix the optical power of the refractive optical unit.

[0014] Step 2-1, set the axial coordinates of the variable metasurface group and the refractive optical element as follows: Fixed image plane coordinates are .

[0015] Step 2-2: Set explicit restricted variables according to the mechanical structure requirements, for example, ... Limited to a preset interval; the remaining internal intervals are obtained according to the remaining length allocation method:

[0016] in, This represents the m-th remaining internal interval. M represents the minimum allowable mechanical spacing of the remaining internal spacing, and M represents the number of remaining internal spacings. This indicates that positive values ​​are assigned weights. This approach allows critical intervals to be directly locked within the acceptable range for the project, while non-critical intervals are retained as flexible assignment variables.

[0017] Steps 2-3 involve parameterizing the optical power of the fixed refractive optical unit. Multiple families with symmetrical positive and negative signs can be used as search entry points to reduce the search resources occupied by obviously unreasonable layouts.

[0018] Step 3: Solve for the state optical power of the cascaded metasurface group involved in zooming based on system-level constraints.

[0019] Step 3-1: For the j-th focal length state, establish the optical power vector of the state to be determined based on the current system topology. Then, solve the system by simultaneously solving for the effective focal length and image plane constraints. The effective focal length and image plane constraints of the system are as follows:

[0020] In the two sets of cascaded metasurface implementations, the state optical power vector can be written as:

[0021] This yields the equivalent optical power locus of each level of the hypersurface group across all focal lengths. Here, h and u represent the height and tilt angle of the edge ray in front of a certain surface, respectively. Let N represent the equivalent optical power of the i-th optical power surface at the j-th target focal length, and N be the index of the last optical power surface.

[0022] Step 4: Perform simultaneous allocation of the system-level third-order aberrations.

[0023] Step 4-1, for the j-th state and the i-th unit with optical power, define the conjugate parameter:

[0024] in, Let represent the angles of inclination of the edge ray as it passes before and after the i-th focal length target at the j-th target focal length. This indicates the height of the marginal ray at the optically potentiometric surface. This indicates the corresponding equivalent optical power. When At that time, take .

[0025] Step 4-2, for each fixed refractive optical unit r, define: ,

[0026] Its third-order aberration contribution satisfies:

[0027] in, This represents the fixed optical power of the r-th fixed refractive optical unit. This represents the third-order aberration parameter to be determined for the fixed refractive optical unit. This is the Seidel auxiliary quantity for the corresponding state.

[0028] Step 4-3: For each cascaded metasurface group k, establish a linearized aberration mapping.

[0029] Step 4-4, convert the Seidel auxiliary quantity into the following form: ,

[0030] In steps 4-5, the intrinsic third-order aberrations of the two sets of variable metasurface groups are not entered into vector x as unknowns, but are incorporated into the constant term vector b as known terms. For the k-th variable metasurface group at the j-th target focal length, the edge ray height, edge ray incident angle, edge ray exit angle, principal ray height, principal ray incident angle, and principal ray exit angle at this variable metasurface group are denoted as follows: Then its intrinsic spherical aberration, coma, and astigmatism field curvature are respectively: , ,

[0031] Therefore, the system-level third-order aberration balance no longer depends solely on the fixed refractive optical unit, but simultaneously reflects the combined effect of the refractive unit and the variable metasurface group on the same system aberration budget; the two sets of variable metasurface groups only enter the right-hand vector b in the form of known eigenaber terms.

[0032] Steps 4-6: Stack the three third-order aberration balance equations for all focal length states to form a linear system:

[0033] Where x is the parameter vector to be determined, and is determined solely by the third-order aberration parameters of each fixed refractive optical unit. , Composition; if the system has a total of N fixed refractive optical units, then G is the coefficient matrix, where each of its three rows corresponds to the spherical aberration balance, coma balance, and astigmatism field curvature balance equations for the same target focal length. Each column corresponds to the coefficients of a certain fixed refractive optical unit parameter in vector x. b is the right-hand constant term vector, which consists of the sum of two parts: the first part is the known constant term of the fixed refractive optical unit in the linearized third-order aberration balance equation, which does not contain any unknowns. , ,

[0034] The second part shows the contributions of the two sets of variable metasurface groups to the intrinsic spherical aberration, coma, and astigmatism field curvature at the corresponding target focal lengths, as illustrated in steps 4-5. , as well as .

[0035] Step 5: Perform physical inverse kinematics on the fixed refractive optical unit.

[0036] Step 5-1: For each fixed refractive optical unit, obtain the following solution based on the linear system:

[0037] And further, we obtain: ,

[0038] As a theoretical criterion for glass, Theoretical refractive index, The bending factor, These are the front surface radius of curvature and the rear surface radius of curvature, respectively. From this, the theoretical refractive index, bending factor, and front and rear surface radii of curvature of the fixed refractive optical unit are obtained. Combined with the outer envelope of the finite field-of-view beam spot, the aperture and thickness targets are determined.

[0039] Step 6: Apply physical realizability constraints and establish a unified evaluation function.

[0040] Step 6-1: To further filter the theoretically solvable candidate structures into engineering-usable candidate structures, this invention applies a uniform physical realizability constraint to all candidate layouts. This constraint includes at least: 1. The equivalent optical power of the two sets of variable metasurface groups remains monotonic as the focal length changes across all target focal lengths; 2. The theoretical refractive index obtained by inverse kinematics of a fixed refractive optical unit must be a finite real number; 3. Calculate the front and rear surface radii of curvature, center thickness, edge thickness, and effective nozzle diameter of the fixed refractive element based on the refractive index, optical power, and curvature factor obtained from the inverse kinematics. The front and rear surface radii of curvature must cover the required nozzle diameter, and the center and edge thicknesses must not be lower than preset lower limits. 4. The minimum axial clearance between adjacent fixed refractive optical units shall not be less than a preset safety value; 5. The principal ray shift and equivalent aperture of the rear variable metasurface group must not exceed the preset upper limit across the entire focal length and field of view.

[0041] Step 6-2, construct the fourth Seidel and the field curvature soft constraint. The fourth Seidel of the refraction group satisfies:

[0042] The field curvature term of the metasurface group is 0.

[0043] Step 6-3, construct the fifth Seidel and the distortion soft constraint. For the j-th target focal length state, the fifth Seidel of the fixed refraction group is:

[0044] The distortion and contribution of the variable metasurface group satisfy:

[0045] The sum of distortions of the entire system at the j-th target focal length is obtained as follows:

[0046] Step 6-4: Establish a unified evaluation function. For each candidate structure, the following unified evaluation function is used:

[0047] in, These are the weighting coefficients; This includes metasurface optical power monotonicity, maximum optical power, theoretical refractive index, and material realizability penalty; This includes the curvature radius covering the aperture, center thickness, edge thickness, net gap between adjacent lenses, true back focal length deviation, and constraints on the aperture of the rear metasurface and the principal ray offset.

[0048] Step 7: Multi-topology filtering and total length range filtering.

[0049] Step 7-1: When the system topology is unknown, a multi-stage global search is preferably performed on each candidate topology. The optimization process is as follows: first, a rapid screening of the fixed refractive optical unit optical power symbol families for each topology is performed; then, a medium-depth search is performed on the selected preferred families; and finally, a fine search is performed on the preferred candidates. When the total system length is also unknown, a coarse search grid is first established within a preset total length range to perform an initial screening of each candidate topology and each candidate optical power symbol family; then, a fine search grid is established around the preferred total length obtained from the initial screening to perform a secondary search. Finally, the final initial structure is output according to the rules of prioritizing strongly feasible candidates, prioritizing those with smaller absolute optical power of the metasurface, and prioritizing those with smaller total penalty values.

[0050] Step 8: Recover the metasurface phase distribution based on the state optical power trajectory.

[0051] Step 8-1: After obtaining the equivalent optical power trajectories of the two sets of variable metasurface groups across all target focal length states, further pure Alvarez phase or Moire phase recovery is performed on each variable metasurface group to obtain the dual-sheet phase distribution and mechanical motion trajectory that can be directly used for device implementation. This allows for the acquisition of polynomial coefficients and mechanical motion trajectory parameters that can be directly input into optical design software for further design optimization.

[0052] Compared with the prior art, the present invention has at least the following beneficial effects: 1. This invention establishes for the first time an analytical initial structure design method for hybrid refractive superzoom systems, filling a methodological gap in this field. While mature Gaussian optical solutions exist for the initial structure design of traditional refractive zoom systems, existing work indicates that "feasible initial structures are extremely rare" for hybrid refractive superzoom systems where cascaded metasurfaces replace axially moving mirror groups, necessitating the use of structural priors such as Galilean telescope splicing to circumvent the solution difficulties. This invention proposes for the first time a complete analytical initial structure design process, directly calculating usable initial structures from design specifications without relying on structural priors, fundamentally solving the problem of initial structure solution for hybrid refractive superzoom systems. 2. Under the conditions of fixed image plane and multi-target focal length, the present invention directly solves the state equivalent optical power trajectory of two sets of variable metasurface groups, which is more suitable for solving system-level initial structure; 3. This invention incorporates the fixed refractive optical unit and the variable metasurface group into the same solution framework at the aberration level: the intrinsic spherical aberration, coma, astigmatism field curvature and distortion contribution of the variable metasurface group participate in the system solution according to the analytical formula in the above steps. The conventional third-order aberration parameters can be directly solved through the model, thereby directly solving the refractive index, radius of curvature and other parameters of the conventional lens. 4. This invention does not stop at the level of "theoretical imaging", but introduces engineering constraints such as refractive index, aperture, thickness, net gap and back focus drift in the initial structural design stage, and further introduces soft constraints of field curvature and distortion, so that the output results can be used more directly as the starting point for subsequent fine optical optimization and device realization. 5. This invention further provides a method for recovering the phase distribution of Alvarez or Moire dual-chips from the system-level state optical power trajectory to the device-level phase distribution, which seamlessly connects the system-level design results with the device-level implementation, reduces the amount of manual conversion work, and provides an end-to-end complete design path from algorithm design to device fabrication. Attached Figure Description

[0053] Figure 1 This is an example diagram of the optical system of the hybrid super zoom optical system described in this invention; Figure 2 This is a flowchart of the initial structure generation method for a hybrid super zoom optical system according to the present invention. Detailed Implementation

[0054] In one example, the hybrid super-refractive zoom optical system is a hybrid super-refractive system comprising two sets of cascaded metasurface zoom units and multiple fixed refractive optical units. The total system length is set to 100-130 mm, the operating wavelength is 1550 nm, the target focal length sequence is [30, 40, 50, 60, 70, 80] mm, and the corresponding full field of view sequence is [22.0, 16.0, 13.0, 10.8, 9.3, 8.2].

[0055] First, the propagation segments in the system are parameterized, and a joint search is performed on the fixed optical power of the fixed refractive optical unit. For each candidate layout, the state-equivalent optical power of the two cascaded metasurface groups involved in the zoom is solved under each focal length state. All candidate structures are sorted according to the rules of prioritizing those satisfying hard constraints, those with smaller absolute optical power of the metasurfaces, and those with smaller total penalty values, and the candidate structure with the highest ranking is selected as the final initial structure. Furthermore, pure Alvarez phase retrieval is performed on the second variable metasurface group. Unlike the first variable metasurface group, the actual illumination area of ​​the second variable metasurface group is no longer directly determined by the entrance square aperture, but is determined by the actual geometric ray tracing results after the combined action of the first variable metasurface group and the preceding solid refractive unit. Using the equivalent optical power of the first variable metasurface group at various focal lengths, the front and rear surface curvature radii, center thickness, and refractive index of the front refractive unit, the principal ray, field edge ray, and on-axis edge ray are traced to the second variable metasurface group to obtain the principal ray offset and beam spot half-side length for each state. Based on this, the true illumination square aperture of the second variable metasurface group is established, and pure Alvarez phase retrieval and Binary 1 coefficient derivation are completed.

Claims

1. A method of initial configuration design of a hybrid folded superzoom optical system, characterized by, The hybrid super-zoom optical system includes a first variable metasurface group, a second variable metasurface group, and multiple fixed refractive optical units disposed before, after, and between the two groups; the method includes the following steps: Step 1: Establish a design schedule, set the total system length, fixed image plane position, target focal length sequence, and half field of view sequence corresponding to each target focal length; Step 2: Establish the candidate system topology, determine the number of fixed refractive optical units in the front group, the number of fixed refractive optical units in the rear group, the initial optical power range of each fixed refractive optical unit, and parameterize the axial spacing between each optical power surface. Step 3: Given the candidate topology and axial layout, solve the state equivalent optical power of the first variable metasurface group and the second variable metasurface group for each target focal length state, so that the target focal length state simultaneously satisfies the target effective focal length constraint and the fixed image plane constraint. Step 4: Based on the paraxial tracing results of the edge rays and principal rays of all target focal length states, construct a system of third-order aberration linear equations across states, and solve for the third-order aberration parameters of each fixed refractive optical unit. Step 5: Based on the third-order aberration parameters obtained in Step 4, solve for the theoretical refractive index, bending factor, front and rear surface curvature radii, aperture diameter, and thickness parameters of each fixed refractive optical unit. Step 6: Apply physical realizability constraints to the candidate structure. The physical realizability constraints include at least the positive optical power constraint of the metasurface state, the monotonic constraint across states, the physical feasibility constraint of the refractive index, the lens aperture and thickness constraint, the net gap constraint between adjacent fixed refractive optical units, and the back focal drift constraint of the image plane. Step 7: Sort the candidate structures that meet or nearly meet the physical realizability constraints according to the preset evaluation index, and output the candidate structure with the optimal target value as the initial structure of the hybrid super-zoom optical system. The output results include at least the axial position of the key surface, the fixed optical power of each fixed refractive optical unit, the equivalent optical power of the two sets of variable metasurface groups under each target focal length state, and the theoretical geometric parameters of each fixed refractive optical unit.

2. The initial structural design method according to claim 1, characterized by, In step 2, under a candidate topology including two fixed refractive optical units in the front group and two fixed refractive optical units in the rear group, the axial coordinates of the first variable metasurface group, the first fixed refractive optical unit in the front group, the second fixed refractive optical unit in the front group, the second variable metasurface group, the first fixed refractive optical unit in the rear group, and the second fixed refractive optical unit in the rear group are set; each is confined within a preset interval, and the remaining internal intervals satisfy...

3. The initial structure generation method according to claim 1, characterized by, In step 3, the paraxial tracing performed on the j-th target focal length state satisfies: ， as well as: , in, Let be the equivalent optical power of the i-th optical power unit at the j-th target focal length, and according to: , The equivalent optical power trajectory of each level of the hypersurface group across all focal lengths is obtained.

4. The initial structure generation method according to claim 1, characterized by, In step 4, a conjugate parameter is defined for the j-th target focal length state and the i-th illuminated focal length unit: , When time, take ; For each fixed refractive optical unit r, the following is defined: , , For each cascaded metasurface zoom unit k, establish a linearized aberration mapping: , , , The third-order aberration balance equations under all target focal length conditions are stacked to form a linear system: , Where x is the parameter vector to be determined, and consists only of the third-order aberration parameters of each fixed refractive optical unit; G is the coefficient matrix, with each of its three rows corresponding to the spherical aberration balance, coma balance, and astigmatic field curvature balance under the same target focal length state, and each column in the matrix corresponding to the coefficients of the parameters of each fixed refractive optical unit in the vector x; b is the constant term vector on the right side, which is composed of the known constant terms of each fixed refractive optical unit in the linearized third-order aberration balance without unknowns, and the intrinsic third-order aberrations of the first variable metasurface group and the second variable metasurface group.

5. The initial structure generation method according to claim 1, characterized by, In step 5, for each fixed refractive optical unit r, calculate: , And further calculations: , , To obtain the theoretical refractive index, bending factor, and front and rear surface radii of curvature of the fixed refractive optical unit.

6. After solving the linear equations and obtaining the theoretical refractive index of each fixed refractive optical unit, soft constraints are further applied to the fourth Seidel and the fifth Seidel, wherein the fourth Seidel of the refractive group satisfies: , For the j-th target focal length state, the refraction contribution of the fifth Seidel and satisfies: , ， This yields the fifth Seidel sum for the entire system:

7. The initial structure generation method according to claim 1, wherein In step 7, a unified evaluation function is established. For each candidate structure, the following unified evaluation function is used: ， in, These are the weighting coefficients; This includes metasurface optical power monotonicity, maximum optical power, theoretical refractive index, and material realizability penalty; This includes the curvature radius covering the aperture, center thickness, edge thickness, net gap between adjacent lenses, true back focal length deviation, and constraints on the aperture of the rear metasurface and the principal ray offset.

8. The initial structural design method of claim 1, wherein Before step 2, a candidate system topology set is established, which includes at least a fixed refractive optical unit and a cascaded metasurface zoom unit.

9. The initial structural design method according to claim 8, characterized in that, For each candidate system topology, a family of positive and negative signs for the optical power of the fixed refractive optical unit is established. A multi-stage global search is performed in the order of fast screening, medium-depth search, and fine search to narrow down the range of optical power of the fixed refractive optical unit and improve the search efficiency of feasible initial structures.

10. The initial structural design method according to claim 8 or 9, characterized in that, When the total length of the system is not fixed in advance, a coarse search grid is first established within the preset total length range to perform a preliminary screening of each candidate system topology and each candidate optical power symbol family; then a fine search grid is established around the preferred total length obtained from the preliminary screening to perform a secondary search, and the initial structure of the final output is determined according to the rules of prioritizing strong feasible candidates, prioritizing the smaller absolute optical power of the metasurface, and prioritizing the smaller total penalty value.

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