CN116205111A - Multi-dimensional multi-channel multiplexing super-surface holographic optimization method based on reverse design - Google Patents
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Abstract
The invention discloses an optimization method of multi-dimensional multi-channel multiplexing super-surface hologram based on reverse design, and belongs to the field of optical hologram. The implementation method of the invention comprises the following steps: enriching and refining a response database of the super atom by using a data interpolation method or a deep learning method; transmitting the intensity of the target image back to the holographic surface to obtain complex amplitude distribution, constructing a loss function by using the reconstructed image and the target image, and calculating gradient distribution by using an accompanying algorithm; optimizing the maximum or minimum value of the loss function by using a nonlinear optimization algorithm, and updating the super-surface parameters; based on optimizing out the geometrical parameters of the super surface, the super surface hologram of the multi-wavelength and multi-polarization channels is realized. According to the invention, the material can be replaced by replacing the super-atomic response database, the near-field or far-field image reconstruction can be realized by replacing the diffraction transmission algorithm, and the reconstruction effect is optimized in the reverse design process. The invention can be applied to the fields of display, imaging, information storage, microscopy and anti-counterfeiting encryption.
Description
Technical Field
The invention relates to an optimization method of a super-surface design, in particular to a method for directly outputting geometric parameters and position information of super atoms forming a super-surface after inputting a target image based on reverse design, belonging to the field of optical holography.
Background
Holographic technology is a very promising information processing technology that can record and reproduce the amplitude and phase information of a light field, and thus is widely used in various fields such as display, imaging, information storage, microscopy, and anti-counterfeit encryption. In the computational hologram technology, devices for encoding complex amplitudes, such as Spatial Light Modulators (SLMs), have the disadvantages of narrow operating bandwidth, small angle of view, realization of only phase-only or amplitude modulation, multi-diffraction order crosstalk and twin images, and the like, and it is difficult for commercial spatial light modulators to realize multi-dimensional holographic multiplexing, which severely limits the application of the holographic technology in daily life.
The super surface is a novel two-dimensional planar metamaterial and is generally composed of a single-layer sub-wavelength-sized metal or dielectric nano antenna array. The characteristic of the specific sub-wavelength pixel resolution of the super surface ensures that the holographic reproduction image generated by the super surface has the advantages of high resolution, large field angle, no multi-level diffraction order crosstalk and the like, and overcomes the defects of holographic display and imaging. The super surface can carry out multi-dimensional and multi-channel regulation and control on the light field, and is very suitable for multi-dimensional light field regulation and control, thereby further expanding the information capacity of the holographic technology. The traditional multi-dimensional multi-channel super-surface holographic design method is characterized in that complex amplitude distribution of a plurality of holograms is obtained through a calculation holographic algorithm, then the complex amplitude distribution is encoded through a searching algorithm by utilizing a super-atom-light field response database obtained through scanning, and finally geometric parameters of each super-atom in the super-surface are obtained. In the traditional design method, the super-atomic structure needs to be searched one by one, the time is long, and the defects of complex holographic algorithm and complex search algorithm exist especially for multi-dimensional multi-channel multiplexing super-surface hologram, so that the traditional super-surface hologram design method has the disadvantages of high mastering threshold, multiple design steps and complex design program.
Disclosure of Invention
Aiming at the problems that the conventional multi-dimensional multi-channel super-surface holographic design method has complex holographic algorithm, time and labor are wasted in searching the super-surface structure and the like, the invention mainly aims to provide the multi-dimensional multi-channel multiplexing super-surface holographic optimization method based on reverse design, and the super-surface distribution corresponding to the complex amplitude distribution of the target image is reversely deduced from the target hologram distribution, so that the precision and the optimization efficiency of the super-surface are effectively improved, and the realization of multi-wavelength and multi-polarization channel super-surface holograms is facilitated.
The aim of the invention is achieved by the following technical scheme.
The invention discloses an optimization method of multi-dimensional multi-channel multiplexing super-surface hologram based on reverse design, which comprises the following steps:
step one: under the incident light with different wavelengths and different polarization states, the electromagnetic simulation method is utilized to scan the geometric parameters of the super atoms used for forming the super surface, obtain the optical response under the corresponding dimension, and construct an optical response database (A xx ，φ xx ) And (A) yy ，φ yy ) Wherein t is xx ＝A xx exp(iφ xx )，t yy ＝A yy exp(iφ yy ). The geometric parameters of the super-atom include the length L of the long axis, the length W of the short axis, the height H of the super-atom and the period length P of the metasurface unit.
Constructing an optical response database based on equation (1)
Step two: and (3) interpolating the optical response data in the optical response database obtained in the step one by using a data interpolation method or a deep learning method, so as to enrich and refine the response database of the super atom. The data in the response database is the corresponding relation between the super-atom geometric parameter and the complex amplitude response data.
Preferably, the chebyshev interpolation is utilized to interpolate the optical response data in the optical response database obtained in the step one, so that the response database of the super atom is enriched and refined.
The scan point (L) i ,W i ,H i ,P i ) For the n-order interpolation point L obtained by using Chebyshev theory i ＝min(L)+(max(L)-min(L))cos((2k-1)/(2n))(k＝1,2,3,...)，W i 、H i And P i The same processing is also performed, and the expression of each term is obtained according to the recurrence relation of the chebyshev polynomial.
And then according to the orthogonality of Chebyshev polynomials, obtaining the coefficient of each term,
wherein f (x) k ) I.e. A or phi obtained by scanning in the step one, finally utilizing
And obtaining an interpolated response 8 database, wherein the response database is the corresponding relation between the geometric dimension and the complex amplitude response data.
Step three: based on the reverse design thought, the error of the complex amplitude distribution of the target image and the reconstructed image distribution is taken as an algorithm iteration criterion, so that a loss function is defined as the complex amplitude distribution U of the target image tp And reconstructing an image complex amplitude distribution U 0p Square of the difference, i.e
The objective function is the same as the expression of the loss function, takes the super-atomic geometric parameter, the wavelength of incident light and the polarization state as variables according to the minimum maximum strategy, and takes the mostThe small optical response reaches a maximum of the objective function, i.e
Wherein->
Lambda is the wavelength of the incident light and p is the polarization state of the incident light, which is the geometrical parameter of the superatom. In order to ensure that the meta-atom geometrical parameters are limited in the range of the meta-atom geometrical parameters in the second step in the iterative solving process, the constraint condition corresponding to the objective function is defined as min (L). Ltoreq.L i ≤max(L),min(W)≤W i ≤max(W),min(H)≤H i ≤max(H),min(P)≤P i And max (P) is not more than, so that a multi-dimensional multi-channel multiplexing super-surface optimization problem is built, and the multi-dimensional multi-channel multiplexing super-surface optimization problem is defined as a first multi-dimensional multi-channel multiplexing super-surface optimization problem.
Step four: and (3) as the objective function in the step (III) has a discontinuous problem, the discontinuous problem is unfavorable for carrying out gradient solving calculation on the objective function. The virtual variable t is introduced into the objective function in the step three to enable the objective function to be continuous, the multi-dimensional multi-channel multiplexing super-surface optimization problem constructed in the step three is converted into a continuous multi-dimensional multi-channel multiplexing super-surface optimization problem which is convenient for gradient calculation, and the continuous multi-dimensional multi-channel multiplexing super-surface optimization problem is defined as a multi-dimensional multi-channel multiplexing super-surface optimization problem II.
The multi-dimensional multi-channel multiplexing super-surface optimization problem is as shown in formulas (4) and (5)
min(L)≤L i ≤max(L) (5)
Step five: under the constraint of the third construction, the number of pixels (N x ,N y ) And determining the division of the sample points on the hologram at the sampling intervalCloth, each sampling point is provided with a super atom, and each super atom geometric parameter is randomly given
(i=1, 2, 3., j=1, 2, 3., ij stands for super-atomic position). Searching corresponding hologram complex amplitude distribution U in the response database after interpolation in the second step according to the distribution of the meta-atom geometric parameters 1p Where p is the p-th channel, p takes both x and y channels, defining p=1, 2. Obtaining the amplitude distribution U of the reconstructed image on the target plane according to the Fresnel diffraction formula 0p 。
The Fresnel diffraction formula is shown as formula (6)
Step six: using the amplitude distribution U of the reconstructed image obtained in step five 0p And a target image amplitude distribution U tp And (3) calculating the value of the loss function by using the loss function constructed in the step (III), and judging whether the calculated value of the loss function meets a set iteration stopping threshold.
Step seven: if the loss function in the step six does not reach the set threshold, calculating gradients of the objective function and the constraint function in the step four by utilizing an accompanying algorithm, inputting gradient information and the objective function into a multi-dimensional multi-channel multiplexing super-surface optimization problem II constructed in the step four, performing iterative optimization settlement on the multi-dimensional multi-channel multiplexing super-surface optimization problem II by adopting a nonlinear convex optimization algorithm, and outputting updated N x ×N y And returning to the fifth iteration until the preset threshold is reached, and outputting the optimal super-atom geometric parameters for holographic imaging, namely realizing multi-dimensional multi-channel multiplexing super-surface optimization based on reverse design.
The method also comprises the step eight of: and D, according to the optimal super-atomic geometric parameters obtained in the step seven, manufacturing a high-precision super-surface for hologram, and applying the super-surface to the fields of display, imaging, information storage, microscopy and anti-counterfeiting encryption, and correspondingly improving the performances of display, imaging, information storage, microscopy and anti-counterfeiting encryption.
The beneficial effects are that:
1. the forward optimization of the traditional multi-dimensional multi-channel multiplexing super-surface needs to search the super-atomic structure one by one, and complex algorithm and multiple steps are needed.
2. The optimization method of the multi-dimensional multi-channel multiplexing super-surface hologram based on reverse design can acquire gradient information of all super-atom corresponding light field distribution by adopting an accompanying algorithm and calculating once, omits a complex process of calculating hologram distribution by using a calculation hologram algorithm, omits a complex process of searching super-atom geometric parameters by using a search algorithm to code holograms, is simpler than the traditional super-surface hologram design method, improves efficiency of multi-dimensional multi-channel multiplexing super-surface optimization, and saves a large amount of time;
3. according to the optimization method for the multi-dimensional multi-channel multiplexing super-surface hologram based on the reverse design, in the setting of an objective function and constraint conditions, the multi-dimensional multi-channel image reconstruction is used as the constraint conditions, and the minimum maximum strategy is adopted, so that the design of the multi-dimensional multi-channel super-surface hologram can be rapidly realized under the condition that a complex holographic algorithm and a search algorithm are not constructed, and compared with the existing super-surface hologram design method, the method is more convenient and rapid, is more suitable for multi-dimensional multiplexing, and achieves higher value.
4. Compared with the traditional holographic method, the optimization method of the multi-dimensional multi-channel multiplexing super-surface holographic based on the reverse design can realize end-to-end design, namely, a user can obtain super-surface distribution only by a target image and a super-atom response database without calculating a large amount of data in a large amount of time, all iterative calculation flows are automatically completed, and the optimization efficiency is greatly improved.
5. Compared with the traditional holographic method, the optimization method based on the reverse-design multi-dimensional multi-channel multiplexing super-surface holographic can realize material replacement through the replacement of the super-atomic response database, and can realize near-field or far-field image reconstruction through the replacement of the diffraction transmission algorithm, and the modularized replacement ensures that the optimization method provided by the invention has wider applicability and improves the use convenience.
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FIG. 1 is a schematic flow diagram of an optimization method of multi-dimensional multi-channel multiplexing super-surface holography based on reverse design;
FIG. 2 is a database of the phase response of the super surface obtained by scanning the length, width and wavelength based on the finite difference method of the time domain, wherein FIG. 2 (a) is a schematic diagram of the super atomic structure adopted, and FIG. 2 (b) is a schematic diagram of the phase response of the super surface at the corresponding wavelength;
FIG. 3 is an example of three transfer functions;
fig. 4 is a chebyshev interpolation schematic diagram, in which fig. 4 (a) is a one-dimensional interpolation schematic diagram, fig. 4 (b) is a two-dimensional interpolation schematic diagram, fig. 4 (b 1) is a schematic diagram before interpolation, and fig. 4 (b 2) is a schematic diagram after interpolation;
FIG. 5 is a schematic flow chart of the embodiment 1 of the present invention;
FIG. 6 is a schematic diagram of the effect of holographic reconstruction of the engineered subsurface in example 1 of the present invention.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the embodiments of the present application more apparent, the present invention will be further and completely described with reference to the embodiments and the accompanying drawings, but the embodiments of the present invention are not limited thereto, and other embodiments obtained by those skilled in the art without making any inventive effort are all within the scope of the present invention.
As shown in fig. 5, this embodiment is illustrated by taking a multi-dimensional multi-channel holographic super-surface design using titanium dioxide as a material based on a fresnel diffraction algorithm as an example. The multi-dimensional multi-channel refers to taking polarization and phase regulation as multi-dimensions and taking x and y double polarization directions as multi-channels.
(1) At the position ofThe incident wavelength is 633nm, the polarization state is x polarization and y polarization, and the time domain finite difference method is utilized to scan the titanium dioxide column under different sizes (long L i Width W i Amplitude and phase responses of the corresponding transmission scattering field in the x-direction and the y-direction, which are highly fixed at 600nm and have a super-atomic period of 400nm, were constructed to construct a response database (A xx ，φ xx ) And (A) yy ，φ yy ) Wherein t is xx ＝A xx exp(iφ xx )，t yy ＝A yy exp(iφ yy )。
(2) The scanning point (L) selected in the step (1) i ，W i ) For the n-order interpolation point L obtained by using Chebyshev theory i The same is done for Wi as for min (L) + (max (L) -min (L)) cos ((2 k-1)/(2 n)) (k=1, 2, 3.) the expression for each term is derived from the recurrence relation of chebyshev polynomials.
And then according to the orthogonality of Chebyshev polynomials, obtaining the coefficient of each term,
wherein f (x) k ) Namely A or phi obtained by scanning in the step (1), and finally utilizing
And obtaining an interpolated response database, wherein the response database is the corresponding relation between the geometric dimension and the complex amplitude response data.
(3) Defining a loss function as a target image amplitude distribution U tp And reconstructing an image amplitude distribution U 0p Square of the difference, i.e
The objective function is as expressed as the loss function, and according to the minimum maximum strategy, the original objective function can be written as +.>
The corresponding constraint condition is that min (L) is less than or equal to L i ≤max(L),min(W)≤W i Max (W) is less than or equal to. Where p=1 is the case where x polarized light is incident on the subsurface to obtain reconstructed image 1, and p=2 is the case where y polarized light is incident on the subsurface to obtain reconstructed image 2. Considering that the objective function is no longer everywhere conductive at this time, the gradient operation of the objective function is not facilitated. The virtual variable t is introduced here and the original objective function is converted into constraint conditions, so that the problem is converted into:
min(L)≤L i ≤max(L) (5)
(4) According to the number of hologram pixels to be designed (N x ,N y ) And determining the distribution of sampling points on the hologram at sampling intervals, placing a super atom at each sampling point, and randomly giving the geometric parameter of each super atom
(i=1, 2, 3., j=1, 2, 3., ij stands for super-atomic position). According to the geometrical parameter distribution, searching the response database after interpolation in the step (2) to obtain the corresponding hologram complex amplitude distribution U 1p Where p is the p-th channel. In this embodiment, p takes x and y channels, and p=1, 2 can be defined. From the fresnel diffraction formula, the amplitude distribution U of the reconstructed image in the target plane can be determined 0p 。
(5) Using the amplitude distribution U of the reconstructed image obtained in step (4) 0p And a target image amplitude distribution U tp Calculating the value of the loss function by utilizing the definition in the step (3), and judging whether the calculated value of the loss function meets the set requirement of stopping calculation;
(6) If the loss function in the step (5) does not reach the set threshold, calculating gradients of the objective function and the constraint function by utilizing an accompanying algorithm, inputting gradient information and the objective function into an optimization solver, optimizing by adopting a nonlinear convex optimization algorithm CCSA, and outputting updated N x ×N y Geometric information of the super atoms.
(7) And (3) repeating the steps (4) - (6) until the loss function value reaches a set threshold value, stopping calculation, outputting the optimized geometric dimension information of each super atom in the super surface, and realizing the super surface holographic design under multiple channels.
While the invention has been described with reference to specific embodiments thereof, it is to be understood that these embodiments are merely illustrative of the principles and applications of the present invention. It is therefore to be understood that numerous modifications may be made to the illustrative embodiments and that other arrangements may be devised without departing from the spirit and scope of the present invention as defined by the appended claims. It should be understood that the different dependent claims and the features described herein may be combined in ways other than as described in the original claims. It is also to be understood that features described in connection with separate embodiments may be used in other described embodiments.
Claims (7)
1. The optimization method of the multi-dimensional multi-channel multiplexing super-surface hologram based on reverse design is characterized by comprising the following steps of: comprises the steps of,
step one: under the incident light with different wavelengths and different polarization states, scanning geometrical parameters of super atoms for forming a super surface by using an electromagnetic simulation method, and obtaining optics in corresponding dimensionsResponse, and constructs an optical response database (a xx ，φ xx ) And (A) yy ，φ yy ) Wherein t is xx ＝A xx exp(iφ xx )，t yy ＝A yy exp(iφ yy ) The method comprises the steps of carrying out a first treatment on the surface of the The geometric parameters of the super atom comprise the length L of the long axis, the length W of the short axis, the height H of the super atom and the period length P of the metasurface unit;
step two: interpolating the optical response data in the optical response database obtained in the first step by using a data interpolation method or a deep learning method, and enriching and refining the response database of the super atom; the data in the response database is the corresponding relation between the super-atom geometric parameter and complex amplitude response data;
step three: based on the reverse design thought, the error of the complex amplitude distribution of the target image and the reconstructed image distribution is taken as an algorithm iteration criterion, so that a loss function is defined as the complex amplitude distribution U of the target image tp And reconstructing an image complex amplitude distribution U 0p Square of the difference, i.e
Step four: the object function in the third step has a discontinuous problem, and the discontinuous problem is unfavorable for carrying out gradient solving calculation on the object function; introducing a virtual variable t into the objective function in the step three to enable the objective function to be continuous, converting the multi-dimensional multi-channel multiplexing super-surface optimization problem constructed in the step three into a continuous multi-dimensional multi-channel multiplexing super-surface optimization problem which is convenient for gradient calculation, and defining the continuous multi-dimensional multi-channel multiplexing super-surface optimization problem as a multi-dimensional multi-channel multiplexing super-surface optimization problem II;
step five: under the constraint of the third construction, the number of pixels (N x ,N y ) And determining the distribution of sampling points on the hologram at sampling intervals, placing a super atom at each sampling point, and randomly giving geometric parameters of each super atom
According to superatomic geometry parametersSearching corresponding hologram complex amplitude distribution U in the response database after interpolation in the second step 1p Wherein p is the p-th channel, p takes x and y two channels, and p=1, 2 is defined; obtaining the amplitude distribution U of the reconstructed image on the target plane according to the Fresnel diffraction formula 0p ；
Step six: using the amplitude distribution U of the reconstructed image obtained in step five 0p And a target image amplitude distribution U tp Calculating the value of the loss function by utilizing the loss function constructed in the step three, and judging whether the calculated value of the loss function meets a set iteration stopping threshold;
step seven: if the loss function in the step six does not reach the set threshold, calculating gradients of the objective function and the constraint function in the step four by utilizing an accompanying algorithm, inputting gradient information and the objective function into a multi-dimensional multi-channel multiplexing super-surface optimization problem II constructed in the step four, performing iterative optimization settlement on the multi-dimensional multi-channel multiplexing super-surface optimization problem II by adopting a nonlinear convex optimization algorithm, and outputting updated N x ×N y And returning to the fifth iteration until the preset threshold is reached, and outputting the optimal super-atom geometric parameters for holographic imaging, namely realizing multi-dimensional multi-channel multiplexing super-surface optimization based on reverse design.
2. The optimization method of multi-dimensional multi-channel multiplexing super-surface hologram based on reverse design according to claim 1, wherein: and step eight, according to the optimal super-atomic geometric parameters obtained in the step seven, manufacturing a high-precision super-surface for holography, and applying the super-surface to the fields of display, imaging, information storage, microscopy and anti-counterfeiting encryption, and correspondingly improving the performances of display, imaging, information storage, microscopy and anti-counterfeiting encryption.
3. The optimization method of multi-dimensional multi-channel multiplexing super-surface hologram based on reverse design according to claim 1 or 2, wherein: in step one, an optical response database is constructed based on the formula (1)
4. The optimization method of multi-dimensional multi-channel multiplexing super-surface hologram based on reverse design according to claim 3, wherein: interpolating the optical response data in the optical response database obtained in the first step by utilizing Chebyshev interpolation, and enriching and refining the response database of the super atom;
the scan point (L) i ,W i ,H i ,P i ) For the n-order interpolation point L obtained by using Chebyshev theory i ＝min(L)+(max(L)-min(L))cos((2k-1)/(2n))(k＝1,2,3,...)，W i 、H i And P i The same processing is also carried out, and the expression of each term is obtained according to the recurrence relation of the Chebyshev polynomial;
and then according to the orthogonality of Chebyshev polynomials, obtaining the coefficient of each term,
wherein f (x) k ) I.e. A or phi obtained by scanning in the step one, finally utilizing
And obtaining an interpolated response database, wherein the response database is the corresponding relation between the geometric dimension and the complex amplitude response data.
5. The optimization method of multi-dimensional multi-channel multiplexing super-surface hologram based on reverse design according to claim 4, wherein: in the third step, the objective function is the same as the expression of the loss function according to the most significantThe minimum maximum strategy takes super-atom geometric parameters, incident light wavelength and polarization state as variables, and takes minimum optical response to reach maximum as an objective function, namely
Wherein->
Is the geometric parameter of the super atom, lambda is the wavelength of the incident light, and p is the polarization state of the incident light; in order to ensure that the meta-atom geometrical parameters are limited in the range of the meta-atom geometrical parameters in the second step in the iterative solving process, the constraint condition corresponding to the objective function is defined as min (L). Ltoreq.L i ≤max(L),min(W)≤W i ≤max(W),min(H)≤H i ≤max(H),min(P)≤P i And max (P) is not more than, so that a multi-dimensional multi-channel multiplexing super-surface optimization problem is built, and the multi-dimensional multi-channel multiplexing super-surface optimization problem is defined as a first multi-dimensional multi-channel multiplexing super-surface optimization problem.
6. The optimization method of multi-dimensional multi-channel multiplexing subsurface hologram based on reverse design according to claim 5, wherein: in the fourth step, the multi-dimensional multi-channel multiplexing super-surface optimization problem is as shown in formulas (4) and (5)
min(L)≤L i ≤max(L) (5)
7. The optimization method of multi-dimensional multi-channel multiplexing subsurface hologram based on reverse design according to claim 6, wherein: in the fifth step, the Fresnel diffraction formula is shown as formula (6)
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Citations (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2000020929A1 (en) * | 1998-10-07 | 2000-04-13 | Ecole Polytechnique Federale De Lausanne (Epfl) | Method and apparatus for simultaneous amplitude and quantitative phase contrast imaging by numerical reconstruction of digital holograms |
| EP2422242A1 (en) * | 2009-04-24 | 2012-02-29 | Ecole Polytechnique Fédérale de Lausanne (EPFL) | A method and apparatus for enhanced spatial bandwidth wavefronts reconstructed from digital interferograms or holograms |
| CN111399088A (en) * | 2020-03-25 | 2020-07-10 | 武汉大学 | Three-channel image display method based on micro-nano polarizer array super-surface |
| KR20200126374A (en) * | 2018-01-29 | 2020-11-06 | 유니버시티 오브 워싱턴 | Systems and Imaging Methods for Meta Surfaces and Full-Color Imaging |
| CN114137814A (en) * | 2021-11-30 | 2022-03-04 | 武汉大学 | Super-surface device for realizing independent holographic image multiplexing and construction method thereof |
| CN114692500A (en) * | 2022-03-31 | 2022-07-01 | 重庆大学 | Deep learning-based complex amplitude type super-surface design method, system and device |
-
2023
- 2023-03-09 CN CN202310222586.5A patent/CN116205111B/en active Active
Patent Citations (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2000020929A1 (en) * | 1998-10-07 | 2000-04-13 | Ecole Polytechnique Federale De Lausanne (Epfl) | Method and apparatus for simultaneous amplitude and quantitative phase contrast imaging by numerical reconstruction of digital holograms |
| US6262818B1 (en) * | 1998-10-07 | 2001-07-17 | Institute Of Applied Optics, Swiss Federal Institute Of Technology | Method for simultaneous amplitude and quantitative phase contrast imaging by numerical reconstruction of digital holograms |
| EP2422242A1 (en) * | 2009-04-24 | 2012-02-29 | Ecole Polytechnique Fédérale de Lausanne (EPFL) | A method and apparatus for enhanced spatial bandwidth wavefronts reconstructed from digital interferograms or holograms |
| KR20200126374A (en) * | 2018-01-29 | 2020-11-06 | 유니버시티 오브 워싱턴 | Systems and Imaging Methods for Meta Surfaces and Full-Color Imaging |
| CN111399088A (en) * | 2020-03-25 | 2020-07-10 | 武汉大学 | Three-channel image display method based on micro-nano polarizer array super-surface |
| CN114137814A (en) * | 2021-11-30 | 2022-03-04 | 武汉大学 | Super-surface device for realizing independent holographic image multiplexing and construction method thereof |
| CN114692500A (en) * | 2022-03-31 | 2022-07-01 | 重庆大学 | Deep learning-based complex amplitude type super-surface design method, system and device |
Non-Patent Citations (2)
| Title |
|---|
| R. OGIER; SRI INTERNATIONAL;: "OSPF Database Exchange Summary List Optimization", IETF RFC5243 * |
| 丁昌林;董仪宝;赵晓鹏;: "声学超材料与超表面研究进展", 物理学报, no. 19 * |
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