Surface composite enhancement method of ferrite and nanocrystal composite magnetic isolation sheet

Abstract

The application discloses a surface composite enhancement method of a ferrite and nanocrystal composite magnetic isolation sheet, and relates to the technical field of material processing, which comprises the following steps: obtaining a surface micrograph, a normal magnetic flux density distribution graph and an infrared temperature rise graph and registering them to a unified coordinate domain; segmenting a defect phase and a solid phase and calculating the narrowest quantity of a window insulation corridor; constructing equivalent surface resistivity according to the quantity; estimating eddy current track wall potential in combination with working conditions; generating a target region by double-threshold decision; inversely deducing the minimum compensation thickness according to geometric expansion; implementing localized enhancement and coverage such as atomic layer deposition in the target region; and releasing the product after re-measurement reaches the standard. Through the same domain evaluation and minimization compensation, the eddy current hot spot can be inhibited, the durability and yield are improved, and thinness and coupling efficiency are considered.

Description

Technical Field

[0001] This invention relates to the field of materials processing technology, specifically to a surface composite reinforcement method for a ferrite and nanocrystal composite magnetic shielding sheet. Background Technology

[0002] Wireless charging and near-field communication devices typically incorporate a magnetic shielding sheet between the transmitter and receiver to guide magnetic flux, suppress leakage flux, reduce eddy current losses in metal components, and stabilize coupling efficiency. Ferrites and nanocrystalline materials are widely used due to their low magnetic loss and excellent magnetic permeability. To balance thinness and durability, the industry commonly adds a dense coating to the surface of the composite magnetic shielding sheet to seal micropores and cracks, and improve resistance to damp heat and abrasion.

[0003] Current surface reinforcement methods mostly employ whole-sheet overlay or full-area pore sealing, with common routes including sol-gel film formation, physical vapor deposition, plasma-enhanced chemical vapor deposition, and atomic layer deposition. While these methods can improve surface density on average, several drawbacks remain in engineering applications: First, surface defects exhibit strong spatial inhomogeneity; pores, pinholes, and fine cracks easily form local conductive channels, causing eddy current accumulation and hot spots under electromagnetic conditions, leading to adhesive layer aging, warping, and performance drift. Second, evaluation caliber often relies on average sheet resistance, average thickness, or global porosity, making it difficult to identify the geometrically critical "bottleneck sites" that determine risk. The lack of specific characterization of the narrowest local insulating channels results in hot spot risks being masked by the mean. Third… Infrared temperature rise, magnetic flux density, and microstructure are usually collected at different times and in different coordinate systems, lacking co-domain registration, making it difficult to establish a one-to-one correspondence between specific defect morphology and magnetocaloric performance; fourth, compensation decisions are mostly based on experience or full-area thickening, which can improve reliability but increases coil spacing, leading to coupling attenuation and efficiency reduction, and is also prone to stress concentration and peeling risks at the compensation edge; fifth, there is a lack of localized compensation closed loop based on a clear threshold, the minimum required thickness cannot be quantified, the retesting and release standards are not uniform, and batch-to-batch consistency is difficult to guarantee.

[0004] In summary, existing technologies still struggle to achieve accurate determination based on co-domain data, quantitative planning addressing geometric bottlenecks, and verifiable local compensation without significantly increasing coil spacing. In particular, they lack a streamlined approach that organically integrates microscopic geometry, surface electrical properties, and electromagnetic operating conditions to simultaneously constrain the safety margin of the insulation channel and the eddy current adhesion driving strength at the window scale. Summary of the Invention

[0005] Based on the shortcomings of the prior art described above, the purpose of this invention is to provide a surface composite reinforcement method for ferrite and nanocrystal composite magnetic shielding sheets to solve the above-mentioned technical problems.

[0006] To achieve the above objectives, the present invention provides the following technical solution: a surface composite reinforcement method for a ferrite and nanocrystal composite magnetic shielding sheet, comprising:

[0007] S1: Obtain surface microscopic images, normal magnetic flux density distribution maps, and infrared temperature rise maps of the same region on the ferrite and nanocrystal composite magnetic shielding sheet, and establish a unified coordinate domain through image registration;

[0008] S2: In the coordinate domain, the surface microscopic image is divided into defect phase and solid phase. The shortest bilateral distance field to the defect boundary is calculated inside the solid phase and the distance field ridge is extracted. The minimum bilateral thickness at the distance field ridge is taken within the window that matches the characteristic scale of the electromagnetic circuit and recorded as the narrowest insulating corridor of the window.

[0009] S3: Construct an equivalent surface resistivity distribution based on the narrowest point of the insulation corridor;

[0010] S4: Based on the operating frequency, normal magnetic flux density, effective metal participation thickness and equivalent surface resistivity, the eddy current power density per unit area within the window is obtained, and the vortex rail adhesion potential is obtained by integrating the window area.

[0011] S5: When the narrowest amount of the insulating corridor is less than the preset safety breakage thickness threshold or the vortex rail wall-attaching potential is greater than the preset wall-attaching potential threshold, a target area mask that needs to be compensated is generated, and the minimum compensation thickness is calculated in reverse based on the geometric expansion principle within the target area.

[0012] S6: Perform local compensation in the target area to make the narrowest amount of the insulation corridor greater than or equal to the safety breakage thickness threshold, and the vortex rail adhesion potential less than or equal to the adhesion potential threshold.

[0013] S7: Conduct a retest to confirm that the narrowest minimum insulation corridor in the entire region is greater than or equal to the safety breakage thickness threshold, and the maximum vortex rail adhesion potential in the entire region is less than or equal to the adhesion potential threshold, thus completing the surface composite reinforcement.

[0014] The present invention is further configured such that, in S1, a Cartesian coordinate system and a unified grid resolution are determined using the surface microscopic image as a reference domain, the infrared temperature rise map and the normal magnetic flux density distribution map are resampled to the unified grid resolution, the translation, rotation and scaling relationships are obtained by edge markers and the corner points of the geometric calibration target to complete the registration, the infrared and magnetic flux density data are written into the corresponding positions of the Cartesian coordinate system, and the data set in the unified coordinate domain is output.

[0015] The present invention is further configured to segment a surface microscopic image into defect phases and solid phases within a coordinate domain, including:

[0016] Brightness equalization and background correction are performed on surface microscopic images within the coordinate domain;

[0017] Anisotropic diffusion or guided filtering is used to suppress high-frequency noise and maintain clear hole and crack edges;

[0018] Particulate contamination is removed by performing small-size morphological opening operations.

[0019] Edge enhancement improves the contrast between hole edges and crack edges, and adaptive threshold segmentation is performed in the local neighborhood to obtain the initial binary image;

[0020] Perform connected component filtering on the initial binary graph, removing isolated micro-points and noisy connected components with excessively small areas;

[0021] After strengthening the slender cracks using a fine-structure enhancement operator, they are incorporated into the defect phase to obtain a binary mask of the defect phase and a binary mask of the complementary solid phase.

[0022] The present invention is further configured such that the calculation of the narrowest amount of the insulating corridor of the window includes:

[0023] Inside the solid phase, calculate the shortest straight-line distance to the nearest defect boundary for each pixel, and form the shortest bilateral distance field by the sum of the shortest straight-line distances on both sides.

[0024] Local maxima are detected on the shortest bilateral distance field and connected along the main extension direction to obtain continuous distance field ridges;

[0025] The window side length is set according to the characteristic scale of the electromagnetic circuit. The bilateral thickness of all ridge points within the window range is retrieved in each window. The minimum bilateral thickness is recorded as the narrowest insulation corridor of the window. The narrowest insulation corridor of each window is mapped to a scalar distribution map corresponding to the center of the window.

[0026] The present invention is further configured such that S3 includes:

[0027] The narrowest value of the insulation corridor is mapped point by point to the surface resistivity measurement value in the same region using a unified grid, thus constructing a mapping relationship between the equivalent surface resistivity and the narrowest value of the insulation corridor.

[0028] The narrowest value of the insulation corridor is adaptively segmented from small to large, and an ordered regression is used to generate a monotonically increasing mapping curve.

[0029] Piecewise smooth monotonic splines are used to interpolate the mapping curve to ensure a continuous transition between different insulation corridor values, thus obtaining an equivalent surface resistivity distribution covering the entire region.

[0030] The present invention is further configured such that S4 includes:

[0031] A monotonic relationship is established, jointly determined by the operating frequency, normal magnetic flux density, effective metal participation thickness, and equivalent surface resistivity. This relationship satisfies that the eddy current power density per unit area increases with increasing operating frequency, increases with increasing normal magnetic flux density, increases with increasing effective metal participation thickness, and decreases with increasing equivalent surface resistivity. The mapping curve and scaling parameters are determined through calibration at a small number of points on a reference sample, and the mapping is solidified into a lookup table or segmented spline form.

[0032] The eddy current power density per unit area is generated grid by grid. For each effective pixel, the corresponding operating frequency, normal magnetic flux density, effective metal participation thickness and equivalent surface resistivity are input, and the mapping is called to obtain the eddy current power density per unit area.

[0033] An analysis window matching the characteristic scale of the electromagnetic circuit is set, and the vortex rail adhesion potential of the window is obtained by summing the effective pixels covered by the window according to the pixel area.

[0034] The present invention is further configured such that S5 includes:

[0035] Window by window comparison: when the narrowest insulation corridor in any window is less than the safety breakage thickness threshold, or the vortex rail adhesion potential in the window is greater than the adhesion potential threshold, the window is marked as a window to be compensated.

[0036] The coverage area of ​​all windows to be compensated is merged into an initial spatial mask, and the initial spatial mask is cleaned up.

[0037] Based on spatial connectivity, the purified mask is divided into several connected regions, and compensation parameters are calculated independently for each connected region.

[0038] Establish the target conditions after compensation, so that the narrowest amount of the insulation corridor at each position is greater than or equal to the safety breakage thickness threshold, and the vortex rail wall-attaching potential is less than or equal to the wall-attaching potential threshold.

[0039] Using the concept of geometric expansion to back-calculate thickness, under the localized coating effect of insulating dense material, the increase in thickness on both sides of the narrowest channel is converted into the coating thickness, and the local gain ratio obtained by the pilot sample is introduced to form a parameter library for different surface morphologies and process types.

[0040] When compensation is triggered only because the minimum amount of the insulation corridor is not up to standard, the difference between the safety breakage thickness threshold and the current minimum amount of the insulation corridor is used as the target increment. The minimum compensation thickness that meets the target condition is deduced by combining the local gain ratio and the relationship between the two sides of the thickening.

[0041] When compensation is triggered solely due to the vortex rail's adhesion potential exceeding the limit, the equivalent surface resistivity increase required to reduce the adhesion potential to the adhesion potential threshold is calculated in reverse based on the established correspondence between electromagnetic and surface electrical and thermal properties, and is converted into the required overlay thickness accordingly.

[0042] When compensation is triggered simultaneously due to the minimum width of the insulation corridor not meeting the standard and the vortex rail wall adhesion potential exceeding the limit, the corresponding required thickness is calculated separately, and the larger value is taken as the minimum compensation thickness at that location.

[0043] The present invention is further configured such that the purification process includes: removing isolated small spots with an area smaller than the minimum repairable unit, filling the holes in the mask, applying one to two rings of buffer expansion to the edge of the mask, and lightly smoothing overly sharp boundaries.

[0044] The present invention is further configured such that, in S6, localization compensation is performed by ultrathin overlay through atomic layer deposition.

[0045] The present invention is further configured to calculate the number of cycles required to reach the minimum compensation thickness based on the nominal coverage rate calibrated by the equipment, perform the full number of cycles in the target area, and implement a linear or stepwise decrease in the outer one or two cycles to form a transition zone.

[0046] This invention provides a surface composite enhancement method for ferrite and nanocrystal composite magnetic shielding sheets. The method involves acquiring surface microscopic images, normal magnetic flux density distribution maps, and infrared temperature rise maps of the same region on the ferrite and nanocrystal composite magnetic shielding sheet, and establishing a unified coordinate domain through image registration. Within this coordinate domain, the surface microscopic images are segmented into defect phases and solid phases. Within the solid phase, the shortest bilateral distance field to the defect boundary is calculated, and the distance field ridge is extracted. The minimum bilateral thickness at the distance field ridge is taken within a window matching the characteristic scale of the electromagnetic circuit, and recorded as the narrowest insulating corridor of the window. An equivalent surface resistivity distribution is constructed based on the narrowest insulating corridor. The method is further refined based on the operating frequency, normal magnetic flux density, effective metal participation thickness, and equivalent surface resistivity. Surface resistivity is used to obtain the eddy current power density per unit area within the window. Integrating over the window area yields the vortex rail adhesion potential. When the narrowest insulating corridor is less than the preset safe chain-break thickness threshold or the vortex rail adhesion potential is greater than the preset adhesion potential threshold, a target area mask requiring compensation is generated. Within the target area, the minimum compensation thickness is calculated using the principle of geometric expansion. Localized compensation is performed in the target area to ensure that the narrowest insulating corridor is greater than or equal to the safe chain-break thickness threshold, and the vortex rail adhesion potential is less than or equal to the adhesion potential threshold. Retesting is conducted to confirm that the minimum narrowest insulating corridor in the entire region is greater than or equal to the safe chain-break thickness threshold, and the maximum vortex rail adhesion potential in the entire region is less than or equal to the adhesion potential threshold, thus completing surface composite reinforcement. The beneficial effects include:

[0047] 1. Physically monotonic electrical mapping: Based on the narrowest amount of the insulation corridor, a monotonically increasing equivalent surface resistivity distribution is constructed, so that geometric improvement can be converted into electrical improvement, which facilitates stable extrapolation and consistent control across batches and operating conditions.

[0048] 2. Evaluation of Window-Level Eddy Current Driving Force: Under the constraints of operating frequency, normal magnetic flux density and effective metal participation thickness, the eddy current power density per unit area is calculated and integrated to obtain the eddy rail adhesion potential. The calculable scalar uniformly measures the driving force for the formation of the adhesion eddy current, which is beneficial for achieving spatial consistency verification with infrared temperature rise.

[0049] 3. Quantifiable back-calculation of minimum compensation thickness: Based on the concept of geometric expansion and pilot calibration gain, the minimum thickness required to meet the standard is directly quantified into process parameters, which ensures both electromagnetic and thermal compliance, controls material and time input, and avoids thickness redundancy caused by overcompensation.

[0050] The above description is only an overview of the technical solution of this application. In order to better understand the technical means of this application and to implement it in accordance with the contents of the specification, and to make the above and other objects, features and advantages of this application more obvious and understandable, the following are specific embodiments of this application. Attached Figure Description

[0051] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. In the drawings:

[0052] Figure 1 The flowchart illustrates a surface composite enhancement method for a ferrite and nanocrystal composite magnetic shielding sheet, as an exemplary embodiment of the present invention. Detailed Implementation

[0053] The embodiments of the present invention will be described below with reference to the accompanying drawings and preferred embodiments. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be understood that the preferred embodiments are only for illustrating the present invention and not for limiting the scope of protection of the present invention.

[0054] It should be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. Therefore, the drawings only show the components related to the present invention and are not drawn according to the actual number, shape and size of the components in the actual implementation. In the actual implementation, the form, quantity and proportion of each component can be arbitrarily changed, and the layout of the components may also be more complex.

[0055] In the following description, numerous details are explored to provide a more thorough explanation of embodiments of the invention. However, it will be apparent to those skilled in the art that embodiments of the invention may be practiced without these specific details. In other embodiments, well-known structures and devices are shown in block diagram form rather than in detail to avoid obscuring embodiments of the invention.

[0056] A surface composite reinforcement method for ferrite and nanocrystal composite magnetic shielding sheets, such as Figure 1 As shown, it includes:

[0057] S1: Obtain surface microscopic images, normal magnetic flux density distribution maps, and infrared temperature rise maps of the same region on the ferrite and nanocrystal composite magnetic shielding sheet, and establish a unified coordinate domain through image registration;

[0058] S2: In the coordinate domain, the surface microscopic image is divided into defect phase and solid phase. The shortest bilateral distance field to the defect boundary is calculated inside the solid phase and the distance field ridge is extracted. The minimum bilateral thickness at the distance field ridge is taken within the window that matches the characteristic scale of the electromagnetic circuit and recorded as the narrowest insulating corridor of the window.

[0059] S3: Construct an equivalent surface resistivity distribution based on the narrowest point of the insulation corridor;

[0060] S4: Based on the operating frequency, normal magnetic flux density, effective metal participation thickness and equivalent surface resistivity, the eddy current power density per unit area within the window is obtained, and the vortex rail adhesion potential is obtained by integrating the window area.

[0061] S5: When the narrowest amount of the insulating corridor is less than the preset safety breakage thickness threshold or the vortex rail wall-attaching potential is greater than the preset wall-attaching potential threshold, a target area mask that needs to be compensated is generated, and the minimum compensation thickness is calculated in reverse based on the geometric expansion principle within the target area.

[0062] S6: Perform local compensation in the target area to make the narrowest amount of the insulation corridor greater than or equal to the safety breakage thickness threshold, and the vortex rail adhesion potential less than or equal to the adhesion potential threshold.

[0063] S7: Conduct a retest to confirm that the narrowest minimum insulation corridor in the entire region is greater than or equal to the safety breakage thickness threshold, and the maximum vortex rail adhesion potential in the entire region is less than or equal to the adhesion potential threshold, thus completing the surface composite reinforcement.

[0064] Specifically, a sample stage with adjustable flatness is used for support and has a three-way fine-tuning self-locking function. It is used in conjunction with a three-axis displacement platform for scanning the normal magnetic flux density and coinciding with the field of view. The repeatability error of the displacement platform is no more than 1 / 5 of the size of one pixel.

[0065] An imaging and measurement module is provided, comprising: an optical or electron microscopy imaging module for acquiring surface microscopic images, capable of distortion calibration and pixel size calibration; a measurement module for acquiring the normal magnetic flux density distribution, comprising an excitation coil, a power supply, a magnetic flux density sensor, and a scanning fixture linked to a displacement platform; and an infrared thermal imaging module for acquiring infrared temperature rise maps, capable of emissivity setting, reflection compensation, and non-uniformity correction.

[0066] A synchronization and calibration unit is set up so that the three types of data acquisition can be completed within the same working window through unified triggering and time recording. A geometric calibration target and an edge marker array are set on the non-working edge of the magnetic shielding sheet for geometric calibration. The arrangement of the markers does not change the magnetothermal characteristics of the functional area.

[0067] The working conditions and acquisition sequence are set and controlled. The excitation frequency, excitation amplitude, ambient temperature and humidity and emissivity parameters are set and kept unchanged in the three types of acquisition. The same fixing method and the same sample posture are used to complete the acquisition of microscopic images and distortion and pixel calibration, scanning of normal magnetic flux density under the same field of view, acquisition of steady-state infrared temperature rise map under the same excitation conditions and completion of emissivity and reflection compensation.

[0068] Using a surface microscopic image as a reference domain, a Cartesian coordinate system and a unified grid resolution are determined. The infrared temperature rise map and normal magnetic flux density distribution map are resampled to the unified grid resolution. Registration is completed by determining translation, rotation, and scaling relationships using edge markers and the corner points of a geometric calibration target. The infrared and magnetic flux density data are then written to their corresponding positions in the Cartesian coordinate system, outputting a data set in the unified coordinate domain. Furthermore, a unified coordinate domain and a unified grid are established. Using the microscopic image as a reference domain, a Cartesian coordinate system and a unified grid resolution are determined. The infrared temperature rise map and normal magnetic flux density distribution map are resampled to the aforementioned resolution. Coarse registration is completed by determining translation, rotation, and scaling relationships using edge markers and the corner points of a geometric calibration target. After geometric correction of the infrared and magnetic flux density data, they are written to the reference domain. Subsequently, dense matching is performed using the mixed features of natural texture and edge markers. Partitioned nonlinear deformation correction is performed within the reference domain while ensuring deformation continuity and monotonicity, thereby establishing a pixel-by-pixel correspondence between the three types of data and outputting a data set in the unified coordinate domain.

[0069] Quality is judged using error and consistency acceptance criteria. The maximum value of the geometric reprojection residual does not exceed half of the reference pixel size, the mean square residual does not exceed 1 / 3 of the reference pixel size, the overlap offset of the outer contour of the functional area does not exceed 1 / 3 of the reference pixel size, the time deviation of the three types of data acquisition does not exceed one sampling period, the infrared emissivity is consistent with the ranging setting, and the zero point and sensitivity of the magnetic flux density sensor are calibrated before the acquisition begins.

[0070] The present invention is further configured to segment a surface microscopic image into defect phases and solid phases within a coordinate domain, including:

[0071] Brightness equalization and background correction are performed on the surface microscopic image within the coordinate domain. Specifically, using the microscopic image as a reference, distortion correction and pixel calibration are completed, and a Cartesian coordinate system and a unified raster are established. The following processing is all performed within this coordinate domain, including brightness equalization and background correction: global grayscale histogram equalization to enhance overall contrast; smoothing filtering with a large window to obtain a low-frequency background image; subtracting the background image from the original image and recalibrating the intensity to ensure the overall grayscale falls within a preset dynamic range, thereby eliminating uneven illumination and slow intensity fluctuations and providing a stable baseline for subsequent threshold segmentation.

[0072] Anisotropic diffusion or guided filtering is used to suppress high-frequency noise while maintaining the clarity of hole and crack edges. Specifically, anisotropic diffusion or guided filtering is used with 3 to 5 iterations and a spatial scale of 1 to 2 pixels to suppress high-frequency particle noise while maintaining a steep grayscale transition between hole and crack edges.

[0073] Small-scale morphological opening operations are performed to remove particulate contamination; specifically, small-scale morphological opening operations are performed on the image: the structuring element is a circle with a radius of 1 to 2 pixels, removing isolated bright spots and tiny dark spots. Subsequently, a preliminary screening of small connected components is performed to remove residual pseudo-spots with an area less than 10 pixels.

[0074] Edge enhancement improves the contrast of hole and crack edges, and adaptive thresholding is performed in the local neighborhood to obtain an initial binary image. Specifically, edge enhancement uses a Laplacian-Gaussian operator to strengthen the edges and enhance the contrast of hole and crack edges. Local thresholding calculates an adaptive threshold within a 31×31 pixel local window, providing higher sensitivity for areas with large intensity variations. An initial binary image is generated, with dark holes, cracks, and uncovered areas classified as defect phases, and the rest as solid phases.

[0075] Connectivity filtering is performed on the initial binary image to remove isolated micro-points and noisy connected regions with too small an area. Specifically, connectivity filtering removes noisy connected regions with an area of ​​less than 30 pixels and retains narrow but continuous slits. Hole correction is performed by performing a single closing operation on gaps that are clearly at the edge of holes to avoid the hole rings being accidentally broken. Boundary consistency is achieved by shielding unreliable segmentation results within a range of 1 to 2 times the window width at the outer edge of the sample.

[0076] After strengthening the slender cracks using a fine-structure enhancement operator, they are incorporated into the defect phase to obtain a defect phase binary mask and a complementary solid phase binary mask. Specifically, a linear fringe enhancement filter is applied to the initial grayscale image, with a scale set to 1 to 3 pixels and a directional response covering 0 to 180 degrees. Fine-line structures with responses exceeding a threshold are incorporated into the defect phase layer to compensate for low-contrast slender cracks. Two complementary binary masks are generated: a defect phase mask and a solid phase mask.

[0077] The present invention is further configured such that the calculation of the narrowest amount of the insulating corridor of the window includes:

[0078] Inside the solid phase, the shortest straight-line distance to the nearest defect boundary is calculated for each pixel, and the sum of the shortest straight-line distances on both sides is used to form the shortest bilateral distance field. Specifically, the Euclidean distance to the nearest defect boundary is calculated inside the solid phase to obtain the unilateral distance field. To avoid false thickening at the boundary, the solid phase is shrunk by 1 to 2 pixels before backprojection before calculating the distance field. The shortest bilateral distance field is defined by the minimum bilateral thickness: inside the solid phase, twice the unilateral distance is used as the approximate bilateral thickness at that point. For asymmetric slits, a bidirectional ray search correction along the normal direction is used, and the sum of the shortest straight-line distances in both directions is taken as the final value.

[0079] Local maxima are detected in the shortest bilateral distance field and connected along the main extension direction to obtain continuous distance field ridges. Specifically, local maxima are detected in the shortest bilateral distance field as candidate ridges. Non-maximum suppression and connectivity are performed according to the gradient direction to form continuous ridges. Bifurcations and burrs are pruned with both length and curvature thresholds to remove short branches with a length of less than 3 pixels or excessive instantaneous curvature, and pseudo ridges with less than 2 pixels close to the defect boundary are removed to ensure that the ridges fall completely inside the solid phase.

[0080] The window side length is set according to the characteristic scale of the electromagnetic circuit. The bilateral thickness of all ridge points within the window range is retrieved in each window. The minimum bilateral thickness is recorded as the narrowest insulation corridor of the window. The narrowest insulation corridor of each window is mapped to a scalar distribution map corresponding to the center of the window. Specifically, the window side length is selected according to the characteristic scale of the electromagnetic circuit. In this embodiment, the window side length corresponding to the working frequency band and structural size is 200 micrometers, approximately 670 pixels; the window sliding step size is 40 micrometers, approximately 133 pixels; the overlap ratio of adjacent windows is approximately 80%, which is used to improve spatial resolution and reduce statistical jumps; incomplete windows are used at the boundaries and the coverage ratio is recorded, and windows with a ratio lower than the set ratio are marked as low confidence; within each window, the bilateral thickness (i.e., the shortest bilateral distance field value corresponding to the point) of all ridge points within the window range is retrieved, and the minimum value is taken as the narrowest insulation corridor of the window. When there are no ridge points in a window, a backup strategy is adopted: the minimum value voting is performed on the shortest bilateral distance field within the window, and the position of the minimum value is locally normal bidirectionally corrected; if there is still no reliable value, the value result of the adjacent window is obtained by spatial interpolation, and the confidence of the window is lowered; the narrowest insulation corridor of each window is assigned to the center coordinate of the window to form a scalar distribution map.

[0081] The present invention is further configured such that S3 includes:

[0082] The narrowest value of the insulation corridor is mapped to the measured surface resistivity of the same domain point by point using a unified grid, thus constructing a mapping relationship between the equivalent surface resistivity and the narrowest value of the insulation corridor. Specifically, four-probe measurements are performed on a unified coordinate domain using an equidistant grid with a measurement point spacing of 1 mm, and the measurement grid corresponds one-to-one with the center of the window. The surface resistivity of each point is recorded with a timestamp and quality label, and sheet resistance is measured. The narrowest value of the insulation corridor at the center of each window is mapped to the measured surface resistivity of the same domain point by point to generate a paired sample set. The corresponding samples are removed based on the criteria of microscopic defocusing, thermal image saturation, and abnormal contact of the four probes. Windows with insufficient coverage and windows without ridges are marked with low confidence and are not included in the modeling for the time being. Several small blocks are selected in dense areas and obvious defect areas, and the typical resistivity ranges at both ends are statistically analyzed for endpoint constraints.

[0083] The narrowest value of the insulation corridor is adaptively segmented from smallest to largest, and ordered regression is used to generate a monotonically increasing mapping curve. Specifically, the narrowest value of the insulation corridor is adaptively segmented from smallest to largest, with an initial number of 10 segments. When the sample size of a segment is lower than a preset lower limit, it is merged with the adjacent segment until the sample size of each segment meets the lower limit. The narrowest value of the insulation corridor is used as the independent variable and the surface resistivity is used as the dependent variable. Monotonically increasing fitting is performed to force the mapping to not decrease in the entire domain. The lower endpoint of the defect reference partition and the upper endpoint of the dense reference partition are used as outer anchor points to limit the convergence range of the mapping at both ends and avoid extrapolation distortion. Outliers with inconsistent local order and poor spatial continuity are removed, and ordered regression is performed again until the residual distribution is stable.

[0084] Piecewise smooth monotonic splines are used to interpolate the mapped curve to ensure a continuous transition between different insulation corridor values, resulting in an equivalent surface resistivity distribution covering the entire domain. Specifically, piecewise smooth monotonic splines are constructed on the piecewise nodes obtained from ordered regression to ensure continuous differentiability between adjacent segments and eliminate the influence of inflection points on the spatial field. The interpolation curvature between adjacent nodes is limited to a preset range to prevent oscillations caused by local overfitting. Equidistant sampling is performed along the entire domain to verify that the interpolation result does not decrease at any adjacent sampling point. If a point violating monotonicity is found, the curvature is automatically tightened and the interpolation is re-performed.

[0085] Substitute the narrowest value of the insulation corridor for each window into the monotonic spline to obtain the corresponding equivalent surface resistivity, forming a window-level resistivity distribution; write the window-level resistivity into a uniform grid, and record the window center coordinates and coverage ratio; perform boundary-preserving light interpolation on low-confidence windows according to spatial neighborhood, and the interpolation is only performed within the same material phase.

[0086] The present invention is further configured such that S4 includes:

[0087] A monotonic relationship determined by the operating frequency, normal magnetic flux density, effective metal participation thickness, and equivalent surface resistivity is established, satisfying that the eddy current power density per unit area increases with increasing operating frequency, normal magnetic flux density, and effective metal participation thickness, and decreases with increasing equivalent surface resistivity. The mapping curve and proportional parameters are determined through calibration at a small number of points on a reference sample, and the mapping is solidified into a lookup table or segmented spline form. Specifically, the reference samples include high-resistivity dense sheets, medium-resistivity sheets, and low-resistivity sheets, all made of the same material as the sample to be tested, and each is fitted with the same type of backplate and adhesive layer. At the same frequency and magnetic flux density as the target operating condition, steady-state temperature rise curves are collected for each type of sample, and the reference value of the eddy current power density per unit area is estimated using the microcalorimetric approximation and steady-state thermal resistance method. Simultaneously, the corresponding normal magnetic flux density, effective participation thickness, and surface resistivity are recorded. The reference data is segmented in an orderly manner according to resistivity from low to high, and a lookup table is established that satisfies the following monotonicity: as frequency increases, the power density per unit area does not decrease; as normal magnetic flux density increases, the power density per unit area does not decrease; as effective participating thickness increases, the power density per unit area does not decrease; as equivalent surface resistivity increases, the power density per unit area does not increase. Piecewise smooth monotonic splines are used to interpolate the lookup table nodes, which are then solidified into a callable mapping. The endpoints are anchored with high magnetic flux density low resistivity samples and high resistivity dense samples to avoid extrapolation distortion.

[0088] The eddy current power density per unit area is generated grid-by-grid. For each valid pixel, the corresponding operating frequency, normal magnetic flux density, effective metal participation thickness, and equivalent surface resistivity are input, and the mapping is called to obtain the eddy current power density per unit area. Specifically, the operating frequency, normal magnetic flux density, effective participation thickness, and equivalent surface resistivity are aligned pixel-by-pixel under a unified grid. Invalid pixels are left blank by masking. For each valid pixel, four parameters are input to the monotonic spline mapping to obtain the eddy current power density per unit area, with the unit being milliwatts per square millimeter. Zero values ​​are returned in regions where the effective participation thickness is zero. Neighborhood consistency checks are performed on obviously isolated abnormally high values. If the difference from the neighborhood exceeds a preset multiple and is not located at the material interface, a low confidence level is marked and replaced with the median value of the neighborhood.

[0089] An analysis window matching the characteristic scale of the electromagnetic circuit is set, and the vortex rail adhesion potential of the window is obtained by summing the pixel areas of the effective pixels covered by the window. Specifically, the side length of the window is 200 micrometers according to the characteristic scale of the electromagnetic circuit; the sliding step size is 40 micrometers, and adjacent windows are allowed to overlap; incomplete windows are allowed at the boundary, and the coverage ratio is recorded at the same time; for the effective pixels covered by each window, the eddy current power density per unit area is summed by the pixel area to obtain the vortex rail adhesion potential of the window.

[0090] The present invention is further configured such that S5 includes:

[0091] Window-by-window comparison: if the narrowest insulation corridor in any window is less than the safe chain break thickness threshold, or the vortex rail adhesion potential in that window is greater than the adhesion potential threshold, then that window is marked as a window to be compensated. Specifically, for each window, if the narrowest insulation corridor is less than the safe chain break thickness threshold, or the vortex rail adhesion potential is greater than the adhesion potential threshold, then it is marked as a window to be compensated. The coverage areas of all windows to be compensated are merged to obtain the initial spatial mask. Incomplete windows are written in a weighted manner according to the coverage ratio.

[0092] The coverage areas of all windows to be compensated are merged into an initial spatial mask, which is then cleaned. Specifically, the cleanup process includes: removing isolated small spots with an area smaller than the minimum repairable unit; filling holes within the mask; applying one to two buffer expansions to the mask edges; and lightly smoothing overly sharp boundaries. Small spot removal: removing isolated spots with an area smaller than the minimum repairable unit (equivalent diameter less than two window steps); hole filling: performing a closing operation on closed holes inside the mask to avoid uncompensated rings; buffer expansion: expanding the mask edges by one to two window steps to cover gaps between windows and provide construction allowance; boundary smoothing: applying light smoothing along the boundaries to suppress sharp corners and facilitate the generation of continuous process paths. The cleaned area mask is then obtained.

[0093] Based on spatial connectivity, the purified mask is divided into several connected regions, and compensation parameters are calculated independently for each connected region. Specifically, the mask is divided into several connected regions according to spatial connectivity, and the circumscribed rectangle, area, perimeter and average curvature of each region are recorded. Based on the distance from the edge and the backing material, it is divided into central and edge regions so as to call different parameter libraries, retrieve similar surface morphology and pore level from the pilot sample library, obtain the gain ratio of geometric thickening to the narrowest amount (denoted as a dimensionless coefficient between 0.5 and 0.8), and record the nominal equivalent thickness of the optional process.

[0094] Establish the target conditions after compensation, so that the narrowest amount of the insulation corridor at each position is greater than or equal to the safe chain breakage thickness threshold, and the vortex rail wall-attaching potential is less than or equal to the wall-attaching potential threshold; specifically, for each position, two conditions must be met simultaneously: the narrowest amount of the insulation corridor is not less than the safe chain breakage thickness threshold; the vortex rail wall-attaching potential is not higher than the wall-attaching potential threshold.

[0095] Using the concept of geometric expansion to back-calculate thickness, under the localized coating effect of insulating dense material, the increase in thickness on both sides of the narrowest channel is converted into the coating thickness, and the local gain ratio obtained by the pilot sample is introduced to form a parameter library for different surface morphologies and process types.

[0096] When compensation is triggered solely due to the insulation corridor's narrowest point not meeting the standard, the target increment is the difference between the safety breakage thickness threshold and the current insulation corridor's narrowest point. The minimum compensation thickness that satisfies the target condition is then derived by combining the local gain ratio and the relationship between the two-sided thickening. Specifically, in the case where the insulation corridor's narrowest point is not meeting the standard, the target increment is calculated as: Δnarrowest point = safety breakage thickness threshold - current narrowest point. Based on the concept of geometric expansion, the contribution of the localized thickening thickness to the two-sided thickness is approximately twice the local gain ratio. The minimum compensation thickness = Δnarrowest point ÷ (2 × local gain ratio). For example, if the current narrowest point of a certain window is 0.08 micrometers, the threshold is 0.12 micrometers, and Δ is 0.04 micrometers; with a local gain ratio of 0.7, the minimum compensation thickness is approximately 0.0286 micrometers, equivalent to 28.6 nanometers.

[0097] When compensation is triggered solely due to the vortex rail's adhesion potential exceeding the limit, the equivalent surface resistivity increase required to reduce the adhesion potential to the threshold is calculated in reverse based on the established correspondence between electromagnetic, surface electrical, and thermal properties, and then converted into the required overlay thickness. Specifically, in the case of the vortex rail's adhesion potential exceeding the limit, the equivalent surface resistivity and normal magnetic flux density of the window are read, and the established monotonic mapping is used to inversely calculate the equivalent surface resistivity increase required to reduce the adhesion potential to the threshold. The required overlay thickness is calculated based on the "resistivity increase curve corresponding to unit overlay thickness" in the process library. If the window is an edge partition, fine adjustments are made according to the edge correction coefficient. For example, if the adhesion potential of a certain window is 15% higher than the threshold, the mapping inverse calculation requires increasing the equivalent surface resistivity from 9 ohms per square meter to 12 ohms per square meter; according to the calibration curve of the atomic layer deposition alumina system, approximately 30 nanometers of overlay is required.

[0098] When compensation is triggered simultaneously due to the insulation corridor's narrowest point not meeting the standard and the vortex rail's wall-attaching potential exceeding the limit, the required thicknesses for each location are calculated, and the larger value is taken as the minimum compensation thickness for that location. Specifically, the required thicknesses for the insulation corridor's narrowest point path and the wall-attaching potential path are calculated separately, and the larger value is taken as the minimum compensation thickness for that window.

[0099] The present invention is further configured such that, in S6, local compensation is performed by atomic layer deposition for ultrathin coating; specifically, the object is a ferrite and nanocrystal composite magnetic shielding sheet, the target area mask and minimum compensation thickness distribution are determined in the pre-process determination, the central connected area requires about 30 nanometers, the edge connected area requires about 20 nanometers; the process temperature is limited to no more than 150 degrees Celsius, and the cavity base pressure is stable within the process requirements range.

[0100] The hard mask is made of stainless steel sheet, laser-formed with windows, and is about 100 micrometers thick; the alignment tolerance is no more than 20 micrometers; a heat-resistant soft mask is applied to non-target areas for secondary protection; one or two transition bands are reserved at the outer edge of the window; double alignment is achieved by edge markings and natural textures to complete clamping and self-locking.

[0101] The substrate was cleaned and dried sequentially with deionized water and isopropanol, then activated with low-power oxygen for no more than 30 seconds to avoid damaging the substrate and bonding interface. The substrate was then loaded into the cavity, evacuated and rinsed with inert gas once each, and stabilized to the set temperature.

[0102] Atomic layer deposition parameter settings: material system is alumina; nominal growth thickness per cycle is approximately 0.11 nm; the timing and duration of metal precursor pulse, oxidant pulse and inert gas flush are set to ensure no cross-contamination and residue; the number of cycles is calculated based on the minimum compensation thickness: 270 cycles are performed in the central connected region and 180 cycles are performed in the edge connected region; the transition zone decreases from the inside to the outside at 50% and 25% respectively.

[0103] Initiate a cycle timer to nucleate and grow in the windowed area; use programmable baffles or partitioned timing to achieve gradual thickness variation in the transition zone; during the process, check the nominal thickness and stability by online elliptic point measurement or quartz crystal point measurement, and pause correction if the deviation exceeds the limit; after deposition, keep the inert gas cooled to a safe temperature and remove the sample.

[0104] The invention is further configured to calculate the number of cycles required to reach the minimum compensation thickness based on the nominal coating rate calibrated by the equipment, execute the full number of cycles within the target area, and implement a linear or stepwise decrease in one or two rings at the outer edge to form a transition zone; specifically, the minimum compensation thickness distribution in the target area is 30 nanometers in the central connected area and 20 nanometers in several edge connected areas; the nominal coating rate of the equipment is calibrated as the nominal growth rate of the alumina system of 0.11 nanometers per cycle, with a stability deviation of no more than 5%; the minimum step size of the equipment is one cycle; the transition zone strategy is to set two transition zones at the outer edge, each with a width of 0.2 millimeters.

[0105] Based on the nominal overlay rate calibrated by the equipment, the number of cycles required to reach the minimum compensation thickness is calculated. For the central connected region: 30 nm divided by 0.11 nm per cycle yields 273 residual cycles, rounded up to 274 cycles. For the edge connected region: 20 nm divided by 0.11 nm per cycle yields 181 residual cycles, rounded up to 182 cycles. Three types of layers are generated based on the target region vector mask: core region, first ring of the transition zone, and second ring of the transition zone. Three types of layers are generated for each connected region to avoid cross-regional crosstalk. The area and perimeter of each layer are recorded for path planning.

[0106] The transition zone reduction strategy is set as follows: Linear reduction example: The core area executes the full number of cycles; the first round executes 60% of the full number of cycles, 274 cycles correspond to 164 cycles, 182 cycles correspond to 110 cycles, and the second round executes 30% of the full number of cycles; 274 cycles correspond to 82 cycles, and 182 cycles correspond to 55 cycles. Stepped reduction example: The core area executes the full number of cycles, the first round executes 70% of the full number of cycles, and the second round executes 40% of the full number of cycles. The two methods should be consistent within the same batch and should not be mixed.

[0107] 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 surface composite reinforcement method for a ferrite and nanocrystal composite magnetic shielding sheet, characterized in that, include: S1: Obtain surface microscopic images, normal magnetic flux density distribution maps, and infrared temperature rise maps of the same region on the ferrite and nanocrystal composite magnetic shielding sheet, and establish a unified coordinate domain through image registration; S2: In the coordinate domain, the surface microscopic image is divided into defect phase and solid phase. The shortest bilateral distance field to the defect boundary is calculated inside the solid phase and the distance field ridge is extracted. The minimum bilateral thickness at the distance field ridge is taken within the window that matches the characteristic scale of the electromagnetic circuit and recorded as the narrowest insulating corridor of the window. S3: Construct an equivalent surface resistivity distribution based on the narrowest point of the insulation corridor; S4: Based on the operating frequency, normal magnetic flux density, effective metal participation thickness and equivalent surface resistivity, the eddy current power density per unit area within the window is obtained, and the vortex rail adhesion potential is obtained by integrating the window area. S5: When the narrowest amount of the insulating corridor is less than the preset safety breakage thickness threshold or the vortex rail wall-attaching potential is greater than the preset wall-attaching potential threshold, a target area mask that needs to be compensated is generated, and the minimum compensation thickness is calculated in reverse based on the geometric expansion principle within the target area. S6: Perform local compensation in the target area to make the narrowest amount of the insulation corridor greater than or equal to the safety breakage thickness threshold, and the vortex rail adhesion potential less than or equal to the adhesion potential threshold. S7: Conduct a retest to confirm that the narrowest minimum insulation corridor in the entire region is greater than or equal to the safety breakage thickness threshold, and the maximum vortex rail adhesion potential in the entire region is less than or equal to the adhesion potential threshold, thus completing the surface composite reinforcement.

2. The surface composite reinforcement method for a ferrite and nanocrystal composite magnetic shielding sheet according to claim 1, characterized in that, In S1, a Cartesian coordinate system and a unified grid resolution are determined using the surface microscopic image as the reference domain. The infrared temperature rise map and the normal magnetic flux density distribution map are resampled to the unified grid resolution. The translation, rotation and scaling relationships are obtained by using edge markers and the corner points of the geometric calibration target to complete the registration. The infrared and magnetic flux density data are written into the corresponding positions in the Cartesian coordinate system, and the data set in the unified coordinate domain is output.

3. The surface composite reinforcement method for a ferrite and nanocrystal composite magnetic shielding sheet according to claim 1, characterized in that, The surface microscopic image is segmented into defect phases and solid phases within the coordinate domain, including: Brightness equalization and background correction are performed on surface microscopic images within the coordinate domain; Anisotropic diffusion or guided filtering is used to suppress high-frequency noise and maintain clear hole and crack edges; Particulate contamination is removed by performing small-size morphological opening operations. Edge enhancement improves the contrast between hole edges and crack edges, and adaptive threshold segmentation is performed in the local neighborhood to obtain the initial binary image; Perform connected component filtering on the initial binary graph, removing isolated micro-points and noisy connected components with excessively small areas; After strengthening the slender cracks using a fine-structure enhancement operator, they are incorporated into the defect phase to obtain a binary mask of the defect phase and a binary mask of the complementary solid phase.

4. The surface composite reinforcement method for a ferrite and nanocrystal composite magnetic shielding sheet according to claim 3, characterized in that, The calculation of the narrowest insulated corridor for the window includes: Inside the solid phase, calculate the shortest straight-line distance to the nearest defect boundary for each pixel, and form the shortest bilateral distance field by the sum of the shortest straight-line distances on both sides. Local maxima are detected on the shortest bilateral distance field and connected along the main extension direction to obtain continuous distance field ridges; The window side length is set according to the characteristic scale of the electromagnetic circuit. The bilateral thickness of all ridge points within the window range is retrieved in each window. The minimum bilateral thickness is recorded as the narrowest insulation corridor of the window. The narrowest insulation corridor of each window is mapped to a scalar distribution map corresponding to the center of the window.

5. The surface composite reinforcement method for a ferrite and nanocrystal composite magnetic shielding sheet according to claim 1, characterized in that, S3 include: The narrowest value of the insulation corridor is mapped point by point to the surface resistivity measurement value in the same region using a unified grid, thus constructing a mapping relationship between the equivalent surface resistivity and the narrowest value of the insulation corridor. The narrowest value of the insulation corridor is adaptively segmented from small to large, and an ordered regression is used to generate a monotonically increasing mapping curve. Piecewise smooth monotonic splines are used to interpolate the mapping curve to ensure a continuous transition between different insulation corridor values, thus obtaining an equivalent surface resistivity distribution covering the entire region.

6. The surface composite reinforcement method for a ferrite and nanocrystal composite magnetic shielding sheet according to claim 1, characterized in that, S4 include: A monotonic relationship is established, jointly determined by the operating frequency, normal magnetic flux density, effective metal participation thickness, and equivalent surface resistivity. This relationship satisfies that the eddy current power density per unit area increases with increasing operating frequency, increases with increasing normal magnetic flux density, increases with increasing effective metal participation thickness, and decreases with increasing equivalent surface resistivity. The mapping curve and scaling parameters are determined through calibration at a small number of points on a reference sample, and the mapping is solidified into a lookup table or segmented spline form. The eddy current power density per unit area is generated grid by grid. For each effective pixel, the corresponding operating frequency, normal magnetic flux density, effective metal participation thickness and equivalent surface resistivity are input, and the mapping is called to obtain the eddy current power density per unit area. An analysis window matching the characteristic scale of the electromagnetic circuit is set, and the vortex rail adhesion potential of the window is obtained by summing the effective pixels covered by the window according to the pixel area.

7. The surface composite reinforcement method for a ferrite and nanocrystal composite magnetic shielding sheet according to claim 1, characterized in that, S5 include: Window by window comparison: when the narrowest insulation corridor in any window is less than the safety breakage thickness threshold, or the vortex rail adhesion potential in the window is greater than the adhesion potential threshold, the window is marked as a window to be compensated. The coverage area of ​​all windows to be compensated is merged into an initial spatial mask, and the initial spatial mask is cleaned up. Based on spatial connectivity, the purified mask is divided into several connected regions, and compensation parameters are calculated independently for each connected region. Establish the target conditions after compensation, so that the narrowest amount of the insulation corridor at each position is greater than or equal to the safety breakage thickness threshold, and the vortex rail wall-attaching potential is less than or equal to the wall-attaching potential threshold. Using the concept of geometric expansion to back-calculate thickness, under the localized coating effect of insulating dense material, the increase in thickness on both sides of the narrowest channel is converted into the coating thickness, and the local gain ratio obtained by the pilot sample is introduced to form a parameter library for different surface morphologies and process types. When compensation is triggered only because the minimum amount of the insulation corridor is not up to standard, the difference between the safety breakage thickness threshold and the current minimum amount of the insulation corridor is used as the target increment. The minimum compensation thickness that meets the target condition is deduced by combining the local gain ratio and the relationship between the two sides of the thickening. When compensation is triggered solely due to the vortex rail's adhesion potential exceeding the limit, the equivalent surface resistivity increase required to reduce the adhesion potential to the adhesion potential threshold is calculated in reverse based on the established correspondence between electromagnetic and surface electrical and thermal properties, and is converted into the required overlay thickness accordingly. When compensation is triggered simultaneously due to the minimum width of the insulation corridor not meeting the standard and the vortex rail wall adhesion potential exceeding the limit, the corresponding required thickness is calculated separately, and the larger value is taken as the minimum compensation thickness at that location.

8. The surface composite reinforcement method for a ferrite and nanocrystal composite magnetic shielding sheet according to claim 7, characterized in that, The cleanup process includes: removing isolated small spots with an area smaller than the minimum repairable unit, filling holes in the mask, applying one to two rings of buffer expansion to the mask edges, and lightly smoothing overly sharp boundaries.

9. The surface composite reinforcement method for a ferrite and nanocrystal composite magnetic shielding sheet according to claim 1, characterized in that, In S6, localization compensation is achieved through ultrathin overlay by atomic layer deposition.

10. The surface composite reinforcement method for a ferrite and nanocrystal composite magnetic shielding sheet according to claim 9, characterized in that, Based on the nominal coverage rate specified by the equipment, calculate the number of cycles required to reach the minimum compensation thickness, perform the full number of cycles in the target area, and implement a linear or stepwise decrease in the outer one or two cycles to form a transition zone.

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