Multi-lens system

Abstract

A system includes: a first lens disposed over a first portion of a respective first surface; and a second lens spaced apart from the first lens along an optical axis of the system and disposed over a second portion of a respective second surface. At least one of the first portion or the second portion does not extend over an entire area of the respective surface configured to receive incident light on the respective surface.

Description

MULTI-LENS SYSTEMTECHNICAL FIELD

[0001] This specification relates to optical systems.BACKGROUND

[0002] Meta optical elements (MOEs), such as metalenses, are optical elements that employ a flat optic technology. Meta optical elements include a metasurface with distributed meta-atoms. Meta-atoms are subwavelength structures (e.g., nanostructures) arranged to interact with light in a particular manner. The meta-atoms can, individually and / or collectively, interact with light waves to change a local amplitude, a local phase, or both, of an incoming light wave. MOEs can be used, for example, in optical applications to take advantage of the flat surface and reduced thickness, compared to classic, curved refractive lenses.

[0003] Lens systems can include multiple lenses to, e.g., improve the quality of a formed image. For example, a first lens in the system can be configured to perform an optical function (e.g., collimate or focus) and a second lens can correct aberrations introduced by the first lens, such as chromatic aberrations or achromatic aberrations (e.g., spherical aberration, coma, etc.). A drawback of conventional multiple-lens systems is loss of light caused by compound losses incurred by several lens elements, as a portion of light is reflected by each lens before forming the final image. When a lens system includes one or more metalenses, the light loss can be more significant as a result of compound light loss due to the diffraction efficiency limitations of metalenses.SUMMARY

[0004] This specification relates to optical systems and imaging systems incorporating optical systems. In general, one or more aspects of the subject matter described in this specification can be embodied in a system including: a first lens disposed over a first portion of a respective first surface; and a second lens spaced apart from the first lens along an optical axis of the system and disposed over a second portion of a respective second surface, wherein at least one of the first portion or the second portion does not extend over an entire area of the respective surface configured to receive incident light on the respective surface.

[0005] These and other aspects can each, optionally, include one or more of the following features. At least one of the first lens or the second lens can be a metalens. The other of the at least one of the first portion or the second portion can substantially extend over the entire area of the respective surface configured to receive incident light on the respective surface. The at least one of the first portion or the second portion that does not extend over the entire respective surface can be disposed in a vicinity of one or more edges of the area of the respective surface configured to receive incident light on the respective surface. At least one of the first portion or the second portion can include a plurality of disjoint regions. The first lens can be configured to focus light incident on the first lens towards a sensor. The second lens can be configured to correct one or more aberrations of light focused by the first lens and incident on the second lens. The second lens can be configured to correct one or more of a spherical aberration, chromatic aberration, or comatic aberration. The second lens can be closer to the sensor than the first lens. The first lens can be closer to the sensor than the second lens. The system can further include a third lens spaced apart from the first and second lens along an optical axis of the system and disposed over a third portion of a respective surface. Optionally, the third portion does not extend over the entire respective surface. The third portion can be disposed in a vicinity of one or more edges of an area of the third surface configured to receive incident light on the third surface. The third portion can be smaller than the second portion.

[0006] In general, one or more aspects of the subject matter described in this specification can be embodied in one or more methods (and also one or more non-transitory computer- readable mediums tangibly encoding a computer program operable to cause one or more processors to perform operations), including: obtaining a target optical performance on a sensor plane; obtaining first geometric data of one or more first regions of a first surface, the one or more first regions forming first respective metaoptical elements; obtaining second geometric data of one or more second regions of a second surface spaced apart from the first surface along an optical axis of the lens system, the one or more second regions forming second respective metaoptical elements; obtaining a respective phase function for each of the one or more first and second regions; performing an iterative numerical optimization to determine modified first and / or second geometric data that minimize a difference between a current optical performance value provided by the first and second metaoptical elements onthe sensor plane and the target optical performance value, wherein performing the iterative numerical optimization includes, for each of a plurality of iterations, determining a difference between the current optical performance value on the sensor plane and the target optical performance value, and when it is determined that the difference between the current optical performance value on the sensor plane and the target optical performance value is higher than a target difference, obtaining modified first geometric data and / or modified second geometric data for respective modified first and / or second geometrical regions, and obtaining modified respective phase functions for the modified first and / or second regions.

[0007] One or more aspects of the subject matter described in this specification can also be embodied in one or more systems including one or more processors; and a computer- readable medium storing instructions that cause the one or more processors to perform operations including: obtaining a target optical performance on a sensor plane; obtaining first geometric data of one or more first regions of a first surface, the one or more first regions forming first respective metaoptical elements; obtaining second geometric data of one or more second regions of a second surface spaced apart from the first surface along an optical axis of the lens system, the one or more second regions forming second respective metaoptical elements; obtaining a respective phase function for each of the one or more first and second regions; performing an iterative numerical optimization to determine modified first and / or second geometric data that minimize a difference between a current optical performance value provided by the first and second metaoptical elements on the sensor plane and the target optical performance value, wherein performing the iterative numerical optimization includes, for each of a plurality of iterations, determining a difference between the current optical performance value on the sensor plane and the target optical performance value, and when it is determined that the difference between the current optical performance value on the sensor plane and the target optical performance value is higher than a target difference, obtaining modified first geometric data and / or modified second geometric data for respective modified first and / or second geometrical regions, and obtaining modified respective phase functions for the modified first and / or second regions.

[0008] These and other aspects can each, optionally, include one or more of the following features. Obtaining modified first and / or second geometrical data and obtaining modified respective phase functions can include performing one or more machine learning processes.The target optical performance can include a target illumination value. The current optical performance can include a current illumination value. Determining the difference between the current optical performance value on the sensor plane and the target optical performance can include determining a difference between the current illumination value and the target illumination value. Determining the difference between the current illumination value and the target illumination value can include performing a simulation to determine the current illumination value. Performing the simulation can include performing a ray tracing simulation. Obtaining the modified first and / or second geometric data can include obtaining modifications for one or more of i) a shape, a size, a location, or a number of the first and / or second regions and / or for one or more of ii) a shape, a size, a location, or number of respective meta-atoms in the first and / or second regions.

[0009] Particular embodiments of the subject matter described in this specification can be implemented to realize one or more of the following advantages. Multi-lens systems with reduced compound light losses can be designed and provided. The systems described herein can enhance the illumination performance of an imaging system that incorporates multiple lens systems. The systems described herein can further or alternatively enhance the overall performance, quality, and / or efficiency of an imaging system. The systems described herein can further or alternatively be incorporated in other types of optical systems.

[0010] The details of one or more embodiments of the subject matter described in this specification are set forth in the accompanying drawings and the description below. Other features, aspects, and advantages of the invention will become apparent from the description, the drawings, and the claims.BRIEF DESCRIPTION OF THE DRAWINGS

[0011] FIG. 1 shows a cross-section of an example of a multi-lens system including two lenses.

[0012] FIGs. 2A, 2B, and 2C show cross-sections of examples of multi-lens systems including two lenses.

[0013] FIGs. 3 A and 3B show cross-sections of examples of multi-lens systems including three lenses.

[0014] FIGs. 4A, 4B, and 4C show cross-sections of examples of multi-lens systems with disjoint lens regions.

[0015] FIG. 5 is a flowchart of a method for designing an optical system.

[0016] FIG. 6 is a schematic diagram of a data processing system including a data processing apparatus, which can be programmed as a client or as a server, and implement the techniques described in this document.

[0017] Like reference numbers and designations in the various drawings indicate like elements.DETAILED DESCRIPTION

[0018] A strategy to correct aberrations produced by a lens includes using a multi-lens system. A first lens can be configured to perform a main optical function (e.g., collimating light or focusing light) and a second lens can be configured to provide a correction to the main optical function imparted by the first lens. For example, the second lens can be configured to correct optical aberrations introduced by the first lens. Drawbacks of conventional multiple lens systems may include loss of light caused by compound losses as a portion of light is reflected by each lens of the multi-lens system forming the final image. The light loss can be more significant when the lens system includes one or more metalenses as a result of the compound light loss due to the diffraction efficiency limitations of metalenses.

[0019] However, aberrations do not occur uniformly over a lens and usually increase towards the edges of the lens. Light rays that impinge on a lens in the vicinity of the edge of the lens are usually more affected by aberrations than light rays that impinge on a lens in or near its center. Aberrations can include, for example, spherical aberration, chromatic aberration, and / or comatic aberrations. Thus, the imaging quality provided by a lens or lens system is usually best at or near a central portion of an image and decreases towards the edges.

[0020] FIG. 1 shows a cross-section of an example of a multi-lens system including two lenses. System 100 includes a first lens 110 disposed over a first portion 115 of a respective first surface 121. A second lens 130 is spaced apart from the first lens 110 along an optical axis 180 of the system and disposed over a second portion 135 of a respective secondsurfacel22. Optical axis 180 can be an axis perpendicular to the first surface 121 and second surface 122.

[0021] At least one of the first portion or the second portion does not extend over an entire area of the respective surface where incident light hits the respective surface. In the example shown in FIG. 1, the second portion 135 does not extend over the entire surface of the second surface 122. For example, the second portion does not extend over a central region 140. In this example, the second portion, (more generally, the at least one of the first portion or the second portion that does not extend over the entire respective surface) is disposed in a vicinity of and / or at 190 one or more edges of the area of the respective surface where incident light hits the respective surface. A central portion of the second lens is “hollow.” For example, the second lens can be ring-shaped. In other examples, the second lens can be of elliptical shape with a hollow central portion.

[0022] The second lens is disposed in areas of the substrate where light rays 162A, 162B hitting the second lens would suffer the most from optical aberrations introduced by the first lens 110. The second lens is disposed in areas of the substrate with high aberration (e.g., at or near the edges) and does not extend over the entire surface of the respective substrate where incident light hits the respective substrate (e.g., does not extend over a central portion). Consequently, the resulting image quality is improved while keeping light losses to a minimum. In some examples, the first lens 110 can be a focusing lens or a lens configured to focus light incident on the first lens towards sensor 105. In some examples, the second lens 130 is configured to correct one or more of a spherical aberration, chromatic aberration, or comatic aberration.

[0023] Although in the example of FIG. 1 the multi-lens system includes a substrate 120, and the first and second lenses are disposed over opposite sides of the substrate, in some examples, the multi-lens system does not require a substrate. In such examples, the first lens and the second lens can be disposed one over the other without a substrate in between the two lenses. In other examples, as shown with reference to FIGs. 2B and 2C below, each lens can be disposed over a respective substrate.

[0024] At least one of the first lens or the second lens can be a metalens. In some examples, at least the lens that does not extend over the entire surface is a metalens. Forexample, the second lens 130 can be a metalens. In other examples, both the first and the second lens are metalenses.

[0025] FIGs. 2A, 2B, and 2C show examples of multi-lens systems including two lenses. At least one of the first lens or the second lens can be a metalens.

[0026] In the example of FIG. 2A, a first lens 210A is disposed over a first portion of a respective first surface 221. A second lens 230A is spaced apart from the first lens 210A along an optical axis 218A of the system and disposed over a second portion of a respective second surface 222. Optical axis 218A can be an axis perpendicular to the first surface 221 and / or second surface 222. In this example, light 260A reaches the second lens 230 A before reaching the second lens 210A, that is, the multi-lens system is configured to be disposed so that that the first lens 210A is closer to the sensor than the second lens 230A. The light direction with respect to the multi-lens system is the same in all the figures unless otherwise stated.

[0027] Light rays hitting central portion 240A, travel through the substrate 220 A, and hit the first lens 240A. Other light rays (i.e., those that would suffer from aberration induced by the first lens if the second lens were not present) hit the second lens 230A, travel through the substrate 220A and then hit the first lens 210A. The first lens 210A can perform a focusing function. The second lens 230A can be configured to correct one or more aberrations.

[0028] FIGs. 2B and 2C show examples of multi-lens systems 200B, 200C with different first and second substrates. In the example of FIG. 2B, substrates 221B, 222B (and, thus, lenses 210B, 230B) are spaced apart along the optical axis 218B. The first lens is disposed over a first portion of a first surface of the first substrate 221B. The second lens 230B is spaced apart from the first lens and disposed over a second portion of a second surface of the second substrate 222B. Optical axis 218B can be an axis perpendicular to the first surface of the first substrate 221B and / or the second surface of the second substrate 222B.

[0029] In this example, the second lens 230B does not extend over a central region 240B of its respective surface of substrate 222B. The second lens 230B is disposed in a vicinity of and / or at one or more edges of an area of the second surface of the second substrate 222B configured to receive incident light on the second surface of the second substrate 222B. The second lens 230B can be placed closer to the sensor than the first lens 210B. In someexamples, the first lens 21 OB can perform a focusing function. In some examples, the second lens 230B can be configured to correct one or more optical aberrations.

[0030] FIG. 2C shows an example where the first and second substrates are different substrates 221 C, 222C spaced apart along the optical axis 218C. Optical axis 218C can be an axis perpendicular to the first surface of the first substrate 221C and / or the second surface of the second substrate 222C. In this example, the second lens 230C does not extend over a central region 240C of its respective surface of substrate 221C. The second lens 230C is disposed at the edges and / or in a vicinity of one or more edges of an area of the surface of the second substrate 222C configured to receive incident light on the second surface of the second substrate 222C.The first lens 210C can be placed closer to the sensor than the second lens 230C. In some examples, the first lens 210C can perform a focusing function. In some examples, the second lens 230C can perform a correcting function.

[0031] FIGs. 3 A and 3B show examples of multi-lens systems including three lenses. At least one of lenses can be a metalens. In some examples, all the lenses of the system that are disposed over portions of their respective surface that do not extend over an entire area of the respective surface where incident light hits the respective substrate can be metalenses. FIGs 3A and 3B include a third lens spaced apart from the first and second lens along an optical axis 318A, 318B of the system and disposed over a third portion of a respective third surface. Optical axis 318A and 318B can be axis perpendicular to the first, second, and / or third surfaces.

[0032] In some examples, the third portion does not extend over the entire respective surface. For example, lens 350A in FIG. 3 A does not extend over the central portion of the surface of substrate 343B. For example, lens 350B in FIG. 3B does not extend over the central portion of the surface of substrate 353B. The second lens 330A, 330B is disposed in the vicinity or at the edges of an area of the respective surface configured to receive incident light on the respective surface. The second lens has a hollow central portion and does not extend over the central portion of its respective surface of its respective substrate 340A, 340B. The third lens 350A, 350B is disposed in the vicinity or at the edges of an area of the respective surface configured to receive incident light on the respective surface. The third lens can have a hollow central portion and does not extend over the central portion of its respective surface of its respective substrate 343 A, 343B. In some examples, as shown inFIGs. 3A and 3B, the third portion over which the third lens is disposed can be smaller than the second portion over which the second lens is disposed. The central portion not covered by the third lens 343 A, 343B can be bigger than the central portion not covered by the second lens 340A, 340B. The third lens can serve as an additional correcting layer to address the areas with higher aberrations without reducing the amount of light reaching the sensor.

[0033] In FIG. 3A, the second lens 330A and the third lens 350A are configured to be closer to the sensor than the first lens 310A. In FIG. 3B, the first lens 31 OB is closer to the sensor than the second 350A and the third 350B lens. In some examples, the second lens 330A, 330B and the third lens 350A, 350B can perform correcting functions, such as aberration correction. The first lens 310A, 31 OB can perform focusing functions. In some examples, the first and the second lens can perform focusing and / or collimating functions and the third lens can perform correcting functions. In some examples, the first and second lenses can extend over the entire area of their respective surfaces of their respective substrates configured to receive light on the respective surface and the third lens can extend over a third portion of a respective surface that does not extend over an entire area of the respective surface configured to receive incident light on the respective surface.

[0034] In some examples, the third substrate can be the same substrate as the second substrate. In some examples, the third substrate can be the same as the second substrate. The third and the second lenses can be disposed over opposite sides of a same substrate, similarly to the first and second lenses in FIG. 1 and in FIG. 2A. In some examples, the third lens and the second lens can be disposed one over the other without requiring any substrate in between the two lenses. In some examples, the first substrate is also not required and the three lenses can be disposed one over the other without any substrate in between them.

[0035] FIGs. 4A, 4B, and 4C show examples of multi-lens systems with disjoint lens regions. Contrary to conventional lenses, metalenses with irregular shapes and / or arrangements are relatively easy to manufacture. This opens the possibility to address very complex lighting situations and achieve complex imaging patterns. FIG. 4A shows a multilens system 400A including two metalenses with disjoint lens regions. FIG. 4B shows a multi-lens system 400A including three metalenses with disjoint lens regions. Although in the examples of FIG. 4A and FIG. 4B all the metalenses in the system include a plurality of disjoint regions, in some examples, one or more of the lenses in the multi-lens system can bea conventional lens, or a metalens such as the ones described with reference to FIGs. 2A. 2B, 2C or FIGs. 3A, 3B.

[0036] The system 400A of FIG. 4A includes a first lens 470A, 471 A disposed over a first portion of a respective first surface of a first substrate and a second lens 480A, 481 A, 482A spaced apart from the first lens along an optical axis 418A of the system and disposed over a second portion of a respective second surface. Optical axis 418A can be an axis perpendicular to the first surface 421 A and / or second surface 422A.

[0037] At least one of the first portion or the second portion does not extend over an entire area of the respective surface configured to receive incident light on the respective surface. In some examples, at least one of the first portion or the second portion can include a plurality of disjoint regions. In the example of FIG. 4A, none of the first portion and the second portions extend over an entire surface of their respective surfaces 421 A, 422A. In the example of FIG. 4A, both the first portion and the second portion include a plurality of disjoint regions. In some examples, one of the first lens or the second lens can perform one optical function and the other of the first lens or the second lens can perform a different optical function. In some cases, one of the first lens and the second lens can perform a correcting function. In some cases, the arrangement of the disjoint portions of the first and the second lenses can be such that the amount of light loss can be minimized while still performing the desired optical functions for the first and the second lenses.

[0038] FIG. 4B shows an example of a lens system 400B comprising three lenses disposed over a first, a second, and a third portion of a respective first, second, and third surfaces. In this example, the lenses are spaced apart from each other along an optical axis 418B of the system. Optical axis 418B can be an axis perpendicular to the first surface 42 IB, second surface 422B, and / or third surface 423B.

[0039] At least one of the first, the second, or the third portions do not extend over an entire area of the respective surface configured to receive incident light on the respective surface. At least one of the first, the second, or the third portions includes disjoint portions. In the example of FIG. 4B, the first portion includes a plurality of disjoint regions 470B, 471B. The second portion includes a plurality of disjoint regions 481B, 482B. The third portion includes a plurality of disjoint regions 490B, 491B. FIG. 4C shows an example of a top viewof a metalens disposed over a portion of the substrate that includes a plurality of disjoint regions 480C, 481C, 482C.

[0040] FIG. 5 is a flowchart of a method 500 for designing an optical system. The optical system can include at least one metaoptical element. For example, the optical system can include at least one metalens. In some examples, the method 500 can be used to design an optical system such as the systems of FIGs. 4A, 4B, 4C, where at least some of the optical elements are disposed over disjoint regions. The method 500 can explore geometric configurations of disjoint regions that meet optical performance requirements and that do not have the constraints imposed by conventional lens shapes and / or arrangements.

[0041] At 502, a target optical performance for the optical system on a sensor plane can be obtained. For example, the target optical performance can include one or more of a target illumination value, a relative illumination, a target modulation transfer function, or a target image distortion.

[0042] At 504, first geometric data of one or more first regions of a first surface, the one or more first regions forming first respective metaoptical elements can be obtained. In some examples, the optical system can include more than one metaoptical element, such as the systems of FIGs. 4A, 4B, 4C. In some examples, second geometric data of one or more second regions of a second surface spaced apart from the first surface along an optical axis of the lens system, the one or more second regions forming second respective metaoptical elements can be obtained at 506. The initially provided first and second geometric data serve as an initial condition to start the design process. In some examples, a plurality of regularly disposed disjoint regions can be used as an initial condition. In some examples, although the system includes two metaoptical elements, one of the two metaoptical elements can be kept fixed while the second metaoptical element is optimized.

[0043] At 508, respective phase functions for each of the one or more first regions are obtained. Initial phase functions that serve as an initial guess to start the design process are obtained. If the system includes one or more second regions, respective phase functions for the second regions can be obtained. In some examples, each region of the one or more first regions has a respective phase function, that can be different from the phase functions of the other regions of the one or more first regions. In some examples, each region of the one ormore second regions has a respective phase function, that can be different from the phase functions of the other regions of the one or more second regions.

[0044] Then, an iterative numerical optimization to determine modified first and / or second geometric data that minimize a difference between a current optical performance value provided by the first and second metaoptical elements on the sensor plane and the target optical performance value can be performed at 505.

[0045] Performing the iterative numerical optimization can include performing a plurality of iterations. For each of the plurality of iterations, the method includes determining 510 a difference between the current optical performance value on the sensor plane and the target optical performance value. The current optical performance can include a current illumination value. Determining the difference between the current optical performance value on the sensor plane and the target optical performance can include determining a difference between the current illumination value and the target illumination value. Determining the difference between the current illumination value and the target illumination value can include performing a simulation to determine the current illumination value. In some examples, the simulation can be a ray tracing simulation.

[0046] If it is determined that the difference between the current optical performance value on the sensor plane and the target optical performance value is higher than a target difference or if a maximum number of iterations has not been reached, the method 500 proceeds to steps 512, 514, 516 to obtain modified first geometric data and / or modified second geometric data for respective modified first and / or second geometrical regions, and obtaining modified respective phase functions for the modified first and / or second regions.

[0047] In some examples, the modified geometric data and / or phase functions can be obtained in agreement with, for example, a gradient descent method. The modified geometric data and / or phase functions can be obtained using one or more machine learning processes. In some examples, a generative design process, a swarm algorithm, or an evolutionary algorithm can be used to obtain modified geometric data and / or phase functions that make the algorithm converge towards the target optical performance.

[0048] Obtaining the modified first and / or second geometric data can include obtaining modifications for one or more of a shape, a size, a location, or a number of the first and / or second regions. Obtaining the modified first and / or second geometric data can additionally oralternative include obtaining modifications for one or more of a shape, a size, a location, or a number of respective meta-atoms in the first and / or second regions.

[0049] In some examples, parameters such as a location of the lenses with respect to the sensor and / or an aperture size are also obtained before starting the optimization 505. In some examples, these parameters are kept fixed during the optimization. In other examples, parameters such as a location of the lenses with respect to the sensor and / or an aperture size can also be variables of the optimization process. In that case, modified locations of the lenses with respect to the sensor and / or a modified aperture size are determined at this stage.

[0050] If it is determined that the difference between the current optical performance value on the sensor plane and the target optical performance value is equal or lower than a target difference or if a maximum number of iterations has been reached, the iterative optimization process ends. At 518, control instructions for use in manufacturing of the optical design can be generated. For example, control instructions for performing one or more manufacturing operations to manufacture the optical system can be generated. In some examples, the control instructions include control instructions to perform lithography operations to manufacture the designed optical system. In some examples, the obtained design can be manufactured using one or more lithography operations.

[0051] FIG. 6 is a schematic diagram of a data processing system including a data processing apparatus 600, which can be programmed as a client or as a server. The data processing apparatus 600 is connected with one or more computers 690 through a network 680. While only one computer is shown in FIG. 6 as the data processing apparatus 600, multiple computers can be used. The data processing apparatus 600 includes various software modules, which can be distributed between an applications layer and an operating system. These can include executable and / or interpretable software programs or libraries, including tools and services of one or more programs 604 that implement the methods as described above. The number of software modules used can vary from one implementation to another. Moreover, the software modules can be distributed on one or more data processing apparatus connected by one or more computer networks or other suitable communication networks.

[0052] The data processing apparatus 600 also includes hardware or firmware devices including one or more processors 612, one or more additional devices 614, a computer readable medium 616, a communication interface 618, and one or more user interfacedevices 620. Each processor 612 is capable of processing instructions for execution within the data processing apparatus 600. In some examples, the processor 612 is a single or multithreaded processor. Each processor 612 is capable of processing instructions stored on the computer readable medium 616 or on a storage device such as one of the additional devices 614. The data processing apparatus 600 uses the communication interface 620 to communicate with one or more computers 690, for example, over the network 680. Examples of user interface devices 620 include a display, a camera, a speaker, a microphone, a tactile feedback device, a keyboard, a mouse, and VR and / or AR equipment. The data processing apparatus 600 can store instructions that implement operations associated with the program(s) described above, for example, on the computer readable medium 616 or one or more additional devices 614, for example, one or more of a hard disk device, an optical disk device, a tape device, and a solid state memory device.

[0053] Embodiments of the subject matter and the functional operations described in this specification can be implemented in digital electronic circuitry, or in computer software, firmware, or hardware, including the structures disclosed in this specification and their structural equivalents, or in combinations of one or more of them. Embodiments of the subject matter described in this specification can be implemented using one or more modules of computer program instructions encoded on a non-transitory computer-readable medium for execution by, or to control the operation of, data processing apparatus. The computer- readable medium can be a manufactured product, such as hard drive in a computer system or an optical disc sold through retail channels, or an embedded system. The computer-readable medium can be acquired separately and later encoded with the one or more modules of computer program instructions, e.g., after delivery of the one or more modules of computer program instructions over a wired or wireless network. The computer-readable medium can be a machine-readable storage device, a machine-readable storage substrate, a memory device, or a combination of one or more of them.

[0054] The term “data processing apparatus” encompasses all apparatus, devices, and machines for processing data, including by way of example a programmable processor, a computer, or multiple processors or computers. The apparatus can include, in addition to hardware, code that creates an execution environment for the computer program in question, e.g., code that constitutes processor firmware, a protocol stack, a database managementsystem, an operating system, a runtime environment, or a combination of one or more of them. In addition, the apparatus can employ various different computing model infrastructures, such as web services, distributed computing and grid computing infrastructures.

[0055] A computer program (also known as a program, software, software application, script, or code) can be written in any suitable form of programming language, including compiled or interpreted languages, declarative or procedural languages, and it can be deployed in any suitable form, including as a stand-alone program or as a module, component, subroutine, or other unit suitable for use in a computing environment. A computer program does not necessarily correspond to a file in a file system. A program can be stored in a portion of a file that holds other programs or data (e.g., one or more scripts stored in a markup language document), in a single file dedicated to the program in question, or in multiple coordinated files (e.g., files that store one or more modules, sub-programs, or portions of code). A computer program can be deployed to be executed on one computer or on multiple computers that are located at one site or distributed across multiple sites and interconnected by a communication network.

[0056] The processes and logic flows described in this specification can be performed by one or more programmable processors executing one or more computer programs to perform functions by operating on input data and generating output. The processes and logic flows can also be performed by, and apparatus can also be implemented as, special purpose logic circuitry, e.g., an FPGA (field programmable gate array) or an ASIC (application-specific integrated circuit).

[0057] Processors suitable for the execution of a computer program include, by way of example, both general and special purpose microprocessors, and any one or more processors of any kind of digital computer. Generally, a processor will receive instructions and data from a read-only memory or a random access memory or both. The essential elements of a computer are a processor for performing instructions and one or more memory devices for storing instructions and data. Generally, a computer will also include, or be operatively coupled to receive data from or transfer data to, or both, one or more mass storage devices for storing data, e.g., magnetic, magneto-optical disks, or optical disks. However, a computer need not have such devices. Moreover, a computer can be embedded in another device, e.g.,a mobile telephone, a personal digital assistant (PDA), a mobile audio or video player, a game console, a Global Positioning System (GPS) receiver, or a portable storage device (e.g., a universal serial bus (USB) flash drive), to name just a few. Devices suitable for storing computer program instructions and data include all forms of non-volatile memory, media and memory devices, including by way of example semiconductor memory devices, e.g., EPROM (Erasable Programmable Read-Only Memory), EEPROM (Electrically Erasable Programmable Read-Only Memory), and flash memory devices; magnetic disks, e.g., internal hard disks or removable disks; magneto-optical disks; and CD-ROM and DVD- ROM disks. The processor and the memory can be supplemented by, or incorporated in, special purpose logic circuitry.

[0058] To provide for interaction with a user, embodiments of the subject matter described in this specification can be implemented on a computer having a display device, e.g., an LCD (liquid crystal display) display device, an OLED (organic light emitting diode) display device, or another monitor, for displaying information to the user, and a keyboard and a pointing device, e.g., a mouse or a trackball, by which the user can provide input to the computer. Other kinds of devices can be used to provide for interaction with a user as well; for example, feedback provided to the user can be any suitable form of sensory feedback, e.g., visual feedback, auditory feedback, or tactile feedback; and input from the user can be received in any suitable form, including acoustic, speech, or tactile input.

[0059] The computing system can include clients and servers. A client and server are generally remote from each other and typically interact through a communication network. The relationship of client and server arises by virtue of computer programs running on the respective computers and having a client-server relationship to each other. Embodiments of the subject matter described in this specification can be implemented in a computing system that includes a back-end component, e.g., as a data server, or that includes a middleware component, e.g., an application server, or that includes a front-end component, e.g., a client computer having a graphical user interface or a browser user interface through which a user can interact with an implementation of the subject matter described is this specification, or any combination of one or more such back-end, middleware, or front-end components. The components of the system can be interconnected by any suitable form or medium of digital data communication, e.g., a communication network. Examples of communication networksinclude a local area network (“LAN”) and a wide area network (“WAN”), an inter-network (e.g., the Internet), and peer-to-peer networks (e.g., ad hoc peer-to-peer networks).

[0060] While this specification contains many implementation details, these should not be construed as limitations on the scope of what is being or may be claimed, but rather as descriptions of features specific to particular embodiments of the disclosed subject matter. Certain features that are described in this specification in the context of separate embodiments can also be implemented in combination in a single embodiment. Conversely, various features that are described in the context of a single embodiment can also be implemented in multiple embodiments separately or in any suitable subcombination.Moreover, although features may be described above as acting in certain combinations and even initially claimed as such, one or more features from a claimed combination can in some cases be excised from the combination, and the claimed combination may be directed to a subcombination or variation of a subcombination.

[0061] Similarly, while operations are depicted in the drawings in a particular order, this should not be understood as requiring that such operations be performed in the particular order shown or in sequential order, or that all illustrated operations be performed, to achieve desirable results. In certain circumstances, multitasking and parallel processing may be advantageous. Moreover, the separation of various system components in the embodiments described above should not be understood as requiring such separation in all embodiments, and it should be understood that the described program components and systems can generally be integrated together in a single software product or packaged into multiple software products.

[0062] While this specification contains many specifics, these should not be construed as limitations on the scope of the disclosure or of what may be claimed, but rather as descriptions of features specific to particular implementations. Certain features described in this specification in the context of separate implementations also may be combined in the same implementation. Conversely, various features described in the context of a single implementation also may be implemented in multiple implementations separately or in any suitable sub-combination. Various modifications can be made to the foregoing examples. Accordingly, other implementations also are within the scope of the claims.

Claims

CLAIMS1. A system comprising: a first lens disposed over a first portion of a respective first surface; and a second lens spaced apart from the first lens along an optical axis of the system and disposed over a second portion of a respective second surface, wherein at least one of the first portion or the second portion does not extend over an entire area of the respective surface configured to receive incident light on the respective surface.

2. The system of claim 1 , wherein at least one of the first lens or the second lens is a metalens.

3. The system of any preceding claim, wherein the other of the at least one of the first portion or the second portion substantially extends over the entire area of the respective surface configured to receive incident light on the respective surface.

4. The system of any preceding claim, wherein the at least one of the first portion or the second portion that does not extend over the entire respective surface is disposed in a vicinity of one or more edges of the area of the respective surface configured to receive incident light on the respective surface.

5. The system of any preceding claim, wherein at least one of the first portion or the second portion comprises a plurality of disjoint regions.

6. The system of claim 1 , wherein the first lens is configured to focus light incident on the first lens towards a sensor.

7. The system of claim 6, wherein the second lens is configured to correct one or more aberrations of light focused by the first lens and incident on the second lens.

8. The system of claim 7, wherein the second lens is configured to correct one or more of a spherical aberration, chromatic aberration, or comatic aberration.

9. The system of any one of claims 6 to 8, wherein the second lens is closer to the sensor than the first lens or wherein the first lens is closer to the sensor than the second lens.

10. The system of any preceding claim, further comprising a third lens spaced apart from the first and second lens along an optical axis of the system and disposed over a third portion of a respective surface.

11. The system of claim 10, wherein the third portion does not extend over the entire respective surface.

12. The system of claim 11, wherein the third portion is disposed in a vicinity of one or more edges of an area of the third surface configured to receive incident light on the third surface.

13. The system of claim 11, wherein the third portion is smaller than the second portion.

14. A computer-implemented method for designing an optical system, the method comprising: obtaining a target optical performance on a sensor plane; obtaining first geometric data of one or more first regions of a first surface, the one or more first regions forming first respective metaoptical elements; obtaining second geometric data of one or more second regions of a second surface spaced apart from the first surface along an optical axis of the lens system, the one or more second regions forming second respective metaoptical elements; obtaining a respective phase function for each of the one or more first and second regions; performing an iterative numerical optimization to determine modified first and / or second geometric data that minimize a difference between a current optical performance value provided by the first and second metaoptical elements on the sensor plane and the target optical performance value, wherein performing the iterative numerical optimization comprises, for each of a plurality of iterations, determining a difference between the current optical performance value on the sensor plane and the target optical performance value, and when it is determined that the difference between the current optical performance value on the sensor plane and the target optical performance value is higher than a target difference, obtaining modified first geometric data and / or modified second geometric data for respective modified first and / or second geometrical regions, and obtaining modified respective phase functions for the modified first and / or second regions.

15. The computer-implemented method of claim 14, wherein obtaining modified first and / or second geometrical data and obtaining modified respective phase functions comprises performing one or more machine learning processes.

16. The method of claim 14, wherein the target optical performance comprises a target illumination value and wherein the current optical performance comprises a current illumination value, and wherein determining the difference between the current optical performance value on the sensor plane and the target optical performance comprises determining a difference between the current illumination value and the target illumination value.

17. The method of claim 16, wherein determining the difference between the current illumination value and the target illumination value comprises performing a simulation to determine the current illumination value.

18. The method of claim 17, wherein performing the simulation comprises performing a ray tracing simulation.

19. The method of claim 14, wherein obtaining the modified first and / or second geometric data comprises obtaining modifications for one or more of i) a shape, a size, a location, or a number of the first and / or second regions and / or for one or more of ii) a shape, a size, a location, or number of respective meta-atoms in the first and / or second regions.

20. A non-transitory computer-readable medium tangibly encoding a computer program operable to cause a processing system to perform operations comprising the method of any one of claims 14 to 19.

21. A system comprising: one or more processors; and a computer-readable medium storing instructions that, when performed, cause the one or more processors to perform operations comprising the method of any one of claims 14 to 19.

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