A rigorous scalar light field computation solving method and system

Abstract

This application belongs to the field of light field display technology, specifically disclosing a rigorous scalar light field calculation and solution method and system. It includes: obtaining the complex amplitude distribution on the source plane; and calculating the rigorous scalar light field distribution on the observation plane based on rigorous scalar diffraction theory and the complex amplitude distribution on the source plane. Based on scalar diffraction theory, this application constructs a light field propagation model for arbitrary propagation distances, avoids approximation errors in geometric correction methods through a rigorous scalar light field propagation method, overcomes the propagation distance constraints of the scalable angular spectrum propagation model, and achieves Abbe diffraction-limited resolution through a phase retrieval algorithm.

Description

Technical Field

[0001] This application belongs to the field of light field propagation technology, especially the field of light field display technology, and more specifically, relates to a rigorous scalar light field calculation and solution method and system. Background Technology

[0002] In practical optical imaging systems, imaging resolution primarily depends on the illumination wavelength, numerical aperture (NA), and imaging factor (k-factor). The Abbe diffraction limit defines the theoretical resolution limit of an ideal imaging system. To approach this limit, current research, in addition to focusing on shortening the wavelength or increasing the numerical aperture, increasingly emphasizes reducing the resolution by optimizing the imaging process. k A rigorous optical field propagation model is needed to approximate the ideal transfer function and achieve diffraction-limited imaging. This model is a necessary condition for realizing the ideal transfer function and a key path to approaching the diffraction limit.

[0003] Coherent diffraction imaging (CDI), with its lensless architecture and theoretically perfect transfer function, is considered a core technology for approaching the Abbe diffraction limit. Existing research shows that CDI resolution has surpassed the traditional limit of the Rayleigh criterion, with some results approaching the Abbe diffraction limit. However, current experimental studies indicate that achieving near-Abbe diffraction-limit resolution with CDI generally relies on the design of optical systems with low numerical apertures.

[0004] To date, no lensless CDI technology with ultra-high NA (>0.8) has been publicly reported. Due to the low numerical aperture of existing systems and the non-ideal characteristics of the imaging process, the lateral resolution of CDI is still limited to about 0.69λ.

[0005] Although patent CN2023109055634 proposes a high-NA diffraction field curvature correction method in an attempt to solve the propagation accuracy problem under high NA, the geometric correction model it uses still has approximate errors. Summary of the Invention

[0006] To address the shortcomings of existing technologies, the purpose of this application is to provide a rigorous scalar optical field calculation method and system, aiming to solve the problem that the imaging resolution cannot approach the Abbe diffraction limit due to insufficient accuracy of existing propagation models.

[0007] To achieve the above objectives, firstly, this application provides a rigorous scalar light field calculation and solution method, including:

[0008] Obtain the complex amplitude distribution on the source plane;

[0009] Based on the rigorous scalar diffraction theory and combined with the complex amplitude distribution on the source plane, the rigorous scalar light field distribution on the observation plane is calculated and solved.

[0010] Preferably, the formula for calculating the strict scalar light field distribution is as follows:

[0011]

[0012]

[0013] in, Represents the complex amplitude distribution on the observation plane. Represents the plane of the object The complex amplitude distribution on the source plane, i.e., the complex amplitude distribution on the source plane. Indicates the wavelength of light. , representing the wave number, , indicating aperture point To the observation point The distance is ∑, where ∑ represents the integration region of the observation plane; Represents the coordinates of the observation plane.

[0014] Preferably, this calculation method is applied to forward diffraction propagation, backward diffraction propagation, optical diffraction imaging, inverse problem phase retrieval, wavefield communication and sensing, or optical calculation and encryption.

[0015] Preferably, when applied to optical diffraction imaging, the acquired light intensity information is corrected using the established scalar light field distribution model, thereby achieving diffraction-limited imaging under any numerical aperture.

[0016] Preferably, the step of correcting the collected light intensity information using the established scalar light field distribution model is as follows:

[0017]

[0018] in, This indicates the corrected light intensity. This indicates the intensity of the collected light. This represents the amplitude of the light field distribution.

[0019] To achieve the above objectives, in a second aspect, this application provides a rigorous scalar light field calculation and solution system, comprising: at least one memory for storing a program; and at least one processor for accessing the program stored in the memory, wherein when the program stored in the memory is accessed, the processor is used to access the scalar light field calculation and solution method as described in the first aspect.

[0020] To achieve the above objectives, in a third aspect, this application provides an imaging system, including an optical path module and an imaging detection module, wherein the optical path module is used to generate and control a coherent illumination light field, acquire the full-angle diffraction light field signal of the sample under the illumination, and transmit the light field to the imaging detection module through the aforementioned strictly scalar light field propagation method; the imaging detection module is used to achieve diffraction-limited imaging under arbitrary numerical aperture through a phase retrieval algorithm.

[0021] It is understood that the beneficial effects of the second and third aspects mentioned above can be found in the relevant descriptions in the first aspect mentioned above, and will not be repeated here.

[0022] Overall, the technical solutions conceived in this application have the following beneficial effects compared with the prior art:

[0023] This application proposes a rigorous scalar light field calculation method, including: obtaining the complex amplitude distribution on the source plane; and calculating the rigorous scalar light field distribution on the observation plane based on rigorous scalar diffraction theory and the complex amplitude distribution on the source plane. Based on scalar diffraction theory, this application constructs a light field propagation model for arbitrary propagation distances, avoids approximation errors in geometric correction methods through a rigorous scalar light field propagation method, and overcomes the propagation distance constraint of the scalable angular spectrum propagation model, achieving Abbe diffraction-limited resolution for the first time. Attached Figure Description

[0024] Figure 1 This is a geometrical schematic diagram of the strictly scalar light field propagation method provided in the embodiments of this application.

[0025] Figure 2 This is a flowchart of a rigorous scalar light field calculation and solution method provided in the embodiments of this application.

[0026] Figure 3 This is a schematic diagram of the diffraction field obtained by the rigorous scalar light field propagation method and the traditional Fraunhofer model, provided in the embodiments of this application.

[0027] Figure 4 The embodiments provided in this application will Figure 3 The diffraction field shown is applied to the reconstructed image obtained by computational imaging. Detailed Implementation

[0028] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0029] In this application, the term "and / or" describes the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent three cases: A existing alone, A and B existing simultaneously, and B existing alone. In this application, the symbol " / " indicates that the related objects are in an "or" relationship, for example, A / B means A or B.

[0030] In this application, the terms "first" and "second," etc., are used to distinguish different objects, not to describe a specific order of objects. For example, "first response message" and "second response message," etc., are used to distinguish different response messages, not to describe a specific order of response messages.

[0031] In this application, the term "electrical connection" can refer to a direct circuit connection or a signal transmission via a communication protocol.

[0032] In the embodiments of this application, the terms "exemplary" or "for example" are used to indicate that something is an example, illustration, or description. Any embodiment or design that is described as "exemplary" or "for example" in the embodiments of this application should not be construed as being more preferred or advantageous than other embodiments or design. Specifically, the use of the terms "exemplary" or "for example" is intended to present the relevant concepts in a specific manner.

[0033] In the description of the embodiments of this application, unless otherwise stated, "multiple" means two or more, for example, multiple processing units means two or more processing units, multiple elements means two or more elements, etc.

[0034] The embodiments of this application are described below with reference to the accompanying drawings.

[0035] In scalar diffraction theory, the rigorous mathematical expression of the Rayleigh-Sommerfeld diffraction formula is given by the following equation:

[0036]

[0037] Depend on Figure 1 According to the geometric relationships, the relative distance between the source plane and the observation plane is... It can be represented as:

[0038]

[0039] Expanding the distance r using Taylor series, we can write it as:

[0040]

[0041] in, and It can be represented as:

[0042]

[0043] Will be retained Substituting the first-order gradient term into the Rayleigh-Sommerfeld diffraction formula yields the light field propagation model for any propagation distance:

[0044]

[0045] in, It can be represented as:

[0046]

[0047] Based on the above, such as Figure 2 As shown, this application provides a rigorous scalar light field calculation and solution method, including:

[0048] Obtain the complex amplitude distribution on the source plane;

[0049] Based on the rigorous scalar diffraction theory and combined with the complex amplitude distribution on the source plane, the rigorous scalar light field distribution on the observation plane is calculated and solved.

[0050] Preferably, the formula for calculating the strict scalar light field distribution is as follows:

[0051]

[0052]

[0053] in, Represents the complex amplitude distribution on the observation plane. Represents the plane of the object The complex amplitude distribution on the source plane, i.e., the complex amplitude distribution on the source plane. Indicates the wavelength of light. , representing the wave number, , indicating aperture point To the observation point The distance is ∑, where ∑ represents the integration region of the observation plane; Represents the coordinates of the observation plane.

[0054] It should be noted that this application eliminates the Ewald sphere effect in high numerical aperture coherent diffraction imaging by replacing the binomial expansion method commonly used in optical field propagation methods with a strict Taylor expansion method. This transforms the optical field propagation method from relying on approximate and complex geometric corrections into a new approach that can be solved by rigorous calculation.

[0055] Preferably, this calculation method is applied to forward diffraction propagation, backward diffraction propagation, optical diffraction imaging, inverse problem phase retrieval, wavefield communication and sensing, or optical calculation and encryption.

[0056] Preferably, when applied to optical diffraction imaging, the acquired light intensity information is corrected using the established scalar light field distribution model, thereby achieving diffraction-limited imaging under any numerical aperture.

[0057] Preferably, the step of correcting the collected light intensity information using the established scalar light field distribution model is as follows:

[0058]

[0059] in, This indicates the corrected light intensity. This indicates the intensity of the collected light. This represents the amplitude of the light field distribution.

[0060] Secondly, this application provides a rigorous scalar light field calculation and solution system, comprising: at least one memory for storing a program; and at least one processor for accessing the program stored in the memory. When the program stored in the memory is accessed, the processor is used to access the scalar light field calculation and solution method as described in the first aspect.

[0061] Thirdly, this application provides an imaging system, including an optical path module and an imaging detection module. The optical path module is used to generate and control a coherent illumination light field, acquire the full-angle diffraction light field signal of the sample under the illumination, and transmit the light field to the imaging detection module through the above-mentioned strictly scalar light field propagation method. The imaging detection module is used to realize diffraction-limited imaging under arbitrary numerical aperture through a phase retrieval algorithm.

[0062] Example

[0063] Figure 3 The diffraction field distribution diagrams generated by the rigorous scalar optical field propagation method of this invention and the traditional Fraunhofer model are presented in comparison. Figure 4 To be Figure 3 The image shown is a reconstructed image after 300 iterations of the diffraction field data using the mPIE algorithm (mixed-state ptychographiciterative engine). Comparison reveals that the reconstructed sample of the diffraction field obtained from the traditional Fraunhofer model exhibits significant resolution degradation. This is because its binomial expansion approximation leads to insufficient light field propagation accuracy, resulting in a deterioration in the sharpness of the stacked diffraction imaging. The reconstructed sample based on the rigorous scalar light field propagation method, by introducing a Taylor series expansion, effectively suppresses reconstruction artifacts and achieves a quantitative improvement in resolution.

[0064] It should be understood that the above-described device is used to execute the methods in the above embodiments. The implementation principle and technical effect of the corresponding program modules in the device are similar to those described in the above methods. The working process of the device can be referred to the corresponding process in the above methods, and will not be repeated here.

[0065] Based on the methods in the above embodiments, this application provides an electronic device that may include a processor, a communications interface, a memory, and a communication bus, wherein the processor, communications interface, and memory communicate with each other via the communication bus. The processor may invoke logical instructions stored in the memory to execute the methods in the above embodiments.

[0066] Furthermore, the logical instructions in the aforementioned memory can be implemented as software functional units and, when sold or used as independent products, can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or a portion of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this application.

[0067] Based on the methods in the above embodiments, this application provides a computer-readable storage medium storing a computer program that, when run on a processor, causes the processor to execute the methods in the above embodiments.

[0068] Based on the methods in the above embodiments, this application provides a computer program product that, when run on a processor, causes the processor to execute the methods in the above embodiments.

[0069] It is understood that the processor in the embodiments of this application can be a central processing unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, transistor logic devices, hardware components, or any combination thereof. A general-purpose processor can be a microprocessor or any conventional processor.

[0070] The method steps in this application embodiment can be implemented in hardware or by a processor executing software instructions. The software instructions can consist of corresponding software modules, which can be stored in random access memory (RAM), flash memory, read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), registers, hard disks, portable hard disks, CD-ROMs, or any other form of storage medium known in the art. An exemplary storage medium is coupled to the processor, enabling the processor to read information from and write information to the storage medium. Of course, the storage medium can also be a component of the processor. The processor and the storage medium can reside in an ASIC.

[0071] In the above embodiments, implementation can be achieved entirely or partially through software, hardware, firmware, or any combination thereof. When implemented using software, it can be implemented entirely or partially as a computer program product. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, all or part of the processes or functions described in the embodiments of this application are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted through the computer-readable storage medium. The computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired (e.g., coaxial cable, fiber optic, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium can be any available medium that a computer can access or a data storage device such as a server or data center that integrates one or more available media. The available medium can be a magnetic medium (e.g., floppy disk, hard disk, magnetic tape), an optical medium (e.g., DVD), or a semiconductor medium (e.g., solid-state disk (SSD)).

[0072] It is understood that the various numerical designations used in the embodiments of this application are merely for the convenience of description and are not intended to limit the scope of the embodiments of this application.

[0073] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of this application and is not intended to limit this application. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this application should be included within the scope of protection of this application.

Claims

1. A rigorous method for calculating and solving scalar light fields, characterized in that, include: Obtain the complex amplitude distribution on the source plane; Based on the rigorous scalar diffraction theory, and combined with the complex amplitude distribution on the source plane, the rigorous scalar light field distribution on the observation plane is calculated and solved. The formula for calculating the strict scalar light field distribution is as follows: in, Represents the complex amplitude distribution on the observation plane. Represents the plane of the object The complex amplitude distribution on the source plane, i.e., the complex amplitude distribution on the source plane. Indicates the wavelength of light. , representing wave number , indicating aperture point To the observation point The distance is ∑, where ∑ represents the integration region of the observation plane; Represents the coordinates of the observation plane.

2. The scalar light field calculation and solution method as described in claim 1, characterized in that, This scalar optical field calculation and solution method can be applied to forward diffraction propagation, backward diffraction propagation, optical diffraction imaging, inverse problem phase retrieval, wave field communication and sensing, or optical calculation and encryption.

3. The scalar light field calculation and solution method as described in claim 2, characterized in that, When applied to optical diffraction imaging, the established scalar light field distribution model is used to correct the collected light intensity information, thereby achieving diffraction-limited imaging under arbitrary numerical aperture.

4. The scalar light field calculation and solution method as described in claim 3, characterized in that, The method of correcting the collected light intensity information using the established scalar light field distribution model is as follows: in, This indicates the corrected light intensity. This indicates the intensity of the collected light.

5. A rigorous scalar optical field calculation and solution system, characterized in that, include: At least one memory for storing programs; At least one processor is configured to access a program stored in the memory, wherein when the program stored in the memory is accessed, the processor is configured to access the scalar light field calculation and solution method as described in any one of claims 1 to 4.

6. An imaging system, characterized in that, It includes an optical path module and an imaging detection module, among which, The optical path module is used to generate and control the coherent illumination light field, collect the full-angle diffraction light field signal of the sample under the illumination, and transmit the light field to the imaging detection module through the scalar light field calculation and solution method as described in claim 3 or 4. The imaging detection module is used to achieve diffraction-limited imaging under arbitrary numerical aperture through a phase retrieval algorithm.

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