Correction of Aberration and Apodization of an Optical System Using a Correction Plate

Abstract

An optical system having aberration correction is disclosed. The optical system may include an illumination source. The optical system may include a detector. The optical system may include one or more focusing optical elements configured to image a sample onto the detector based on illumination from the illumination source. The optical system may include two or more aberration correction plates located at one or more pupil planes of the one or more focusing optical elements. The two or more aberration correction plates may provide at least partial correction of two or more linearly independent aberration terms. Any particular one of the two or more aberration correction plates may have a spatially varying thickness profile and provide a selected amount of correction for a single particular aberration term of the two or more linearly independent aberration terms.

Description

Technical Field

[0001] The present disclosure generally relates to correcting wavefront deformations, and more particularly to correcting wavefront deformations using one or more aberration correction plates.

Background Art

[0002] Cross-reference to Related Applications This application claims the benefit of U.S. Provisional Application No. 63 / 144,996, filed on Feb. 3, 2021, entitled "CORRECTION PLATES OF LOW-ORDER ZERNIKE ABERRATIONS AND APODIZATION FOR A HIGH NA IMAGING SYSTEM", with inventors Haifeng Huang, Rui-Fang Shi, Joseph Walsh, Mitchell Lindsay, and Eric Vella, under 35 U.S.C. § 119(e), the entire disclosure of which is incorporated herein by reference.

[0003] In optical inspection or measurement in the semiconductor industry, measurements can be generated based on the collection of light from a sample using a diffraction-limited high numerical aperture (NA) system.

Prior Art Documents

Patent Documents

[0004]

Patent Document 1

Summary of the Invention

Problems to be Solved by the Invention

[0005] As semiconductor devices are miniaturized, the requirements for optical inspection or measurement during the manufacturing process are increasing. In particular, precise aberration control of the wavefront profile is required.

Means for Solving the Problems

[0006] According to one or more embodiments of the present disclosure, an optical system with aberration correction is disclosed. The system includes an illumination source. The system includes a detector. The system includes one or more condenser optical elements configured to image a sample onto the detector based on illumination from the illumination source. The system includes two or more aberration correction plates located at one or more pupil planes of the one or more condenser optical elements, which provide at least partial correction of two or more linearly independent aberration terms, where any particular one of the two or more aberration correction plates has a spatially varying thickness profile and provides a selected amount of correction for a single particular aberration term of the two or more linearly independent aberration terms.

[0007] In some embodiments, the system may further include at least one apodization correction plate configured to at least partially correct apodization.

[0008] In some embodiments, at least one of the two or more aberration correction plates may be configured to at least partially correct apodization.

[0009] In some embodiments, at least one of the two or more aberration correction plates may be configured to at least partially correct apodization, which may be because at least one of the two or more aberration correction plates is an apodization coating configured to vary the transmittance radially according to a radially varying function in which the transmittance increases from the center of the pupil of the optical system to the outer edge of the pupil when at least one of the aberration correction plates is disposed at the pupil plane of the optical system.

[0010] In some embodiments, two or more aberration correction plates may include a first aberration correction plate configured to at least partially correct a first aberration term characterizing a first type of aberration, and a second aberration correction plate configured to at least partially correct a second aberration term characterizing a second type of aberration. In some embodiments, at least one of the first type of aberration or the second type of aberration may be one of astigmatism, coma, spherical aberration, or trefoil aberration.

[0011] In some embodiments, two or more aberration correction plates may further include a third aberration correction plate configured to at least partially correct a third aberration term of two or more linearly independent aberration terms. In some embodiments, the third aberration term can characterize a third type of aberration of the optical system, where the third type of aberration, the second type of aberration, and the first type of aberration are different.

[0012] In some embodiments, the third type of aberration may be spherical aberration.

[0013] In some embodiments, the first aberration correction plate may be configured to at least partially correct the first aberration term when the first aberration correction plate is located on one or more pupil planes of the optical system, and the second aberration correction plate may be configured to at least partially correct the second aberration term when the second aberration correction plate is located on one or more pupil planes of the optical system.

[0014] In some embodiments, the first aberration correction plate may be configured to at least partially correct the first aberration term when the first aberration correction plate is located on a first pupil plane of one or more pupil planes, and the second aberration correction plate may be configured to at least partially correct the second aberration term when the second aberration correction plate is located on a second pupil plane different from the first pupil plane of one or more pupil planes.

[0015] In some embodiments, each of the two or more linearly independent aberration terms may be a Zernike term.

[0016] In some embodiments, each of two or more linearly independent aberration terms may be a lower-order Zernike term within a span including from Zernike term 5 to Zernike term 9.

[0017] In some embodiments, the optical system can be an imaging tool.

[0018] In some embodiments, any aberration correction plate including an aberration term characterizing an aberration type of astigmatism, coma, or trefoil aberration can be rotated and configured to align with the orientation of the aberration type within the optical system.

[0019] In some embodiments, any aberration correction plate located on one or more pupil planes can be arranged within a distance range from the one or more pupil planes, where the distance range can be configured to perform aberration correction within a selected tolerance.

[0020] According to one or more embodiments of the present disclosure, a system with aberration correction is disclosed. The system includes an illumination source. The system includes a detector. The system includes one or more condenser optical elements configured to image a sample onto the detector based on illumination from the illumination source. The system includes a catalog of aberration correction plates. The catalog includes two or more sets. Each of the two or more sets includes two or more aberration correction plates that provide at least partial correction of a specific linearly independent aberration term. Any particular one of the two or more aberration correction plates has a spatially varying thickness profile that provides a selected amount of correction for a specific linearly independent aberration term among the two or more linearly independent aberration terms. Each set corrects a different specific linearly independent aberration term. The optical system includes a selected combination of two or more aberration correction plates and at least partially corrects aberrations within a selected tolerance. Each aberration correction plate in the selected combination is an aberration correction plate from one of the two or more sets.

[0021] In some embodiments, the catalog may further include an apodization set configured to at least partially correct the apodization, and the selected combination may include an apodization correction plate of the apodization set.

[0022] In some embodiments, at least one aberration correction plate of the selected combination may be configured to at least partially correct the apodization.

[0023] In some embodiments, at least one aberration correction plate may be configured to at least partially correct the apodization, because at least one aberration correction plate may include an apodization coating in at least one embodiment, and the apodization coating may be configured to radially vary the transmittance according to a radial variation function in a state where the transmittance from the center of the pupil of the optical system increases with respect to the outer edge of the pupil when at least one aberration correction plate is disposed on the pupil plane of the optical system.

[0024] In some embodiments, the selected combination is adjustable and may provide different configurations of the optical system.

[0025] In some embodiments, the optical system may be an imaging tool.

[0026] In some embodiments, the plurality of aberration terms may include spherical aberration.

[0027] In some embodiments, the plurality of aberration terms may include coma aberration.

[0028] According to one or more embodiments of the present disclosure, a method for correcting aberrations of an optical system is disclosed. The method includes determining the wavefront aberration of the optical system. The method includes providing two or more aberration correction plates for the optical system. Each of the two or more aberration correction plates is configured to at least partially correct one of a plurality of aberration terms. Each of the plurality of aberration terms is linearly independent of each other and is configured to characterize the type of aberration, and each aberration term characterizes the type of aberration of the optical system and is based on the determined wavefront aberration.

[0029] In some embodiments, at least one of the two or more aberration correction plates may be configured to at least partially correct apodization.

[0030] In some embodiments, at least one aberration correction plate may be configured to at least partially correct apodization because the at least one aberration correction plate may include an apodization coating, and the apodization coating is configured to radially vary the transmittance according to a radial variation function in a state where the transmittance from the center of the pupil of the optical system increases toward the outer edge of the pupil when the at least one aberration correction plate is disposed on the pupil plane of the optical system.

[0031] In some embodiments, determining may include measuring the wavefront aberration of the optical system.

[0032] In some embodiments, determining may include simulating the wavefront aberration of the optical system.

[0033] In some embodiments, each of the plurality of aberration terms may be a Zernike term.

[0034] In some embodiments, the plurality of aberration terms may include at least one of astigmatism, coma, spherical aberration, or trefoil aberration.

[0035] In some embodiments, the first type of aberration of the first aberration correction plate among two or more aberration correction plates may be one of astigmatism, coma, spherical aberration, or trefoil aberration.

[0036] In some embodiments, the second type of aberration of the second aberration correction plate among two or more aberration correction plates may be one of astigmatism, coma, spherical aberration, or trefoil aberration.

[0037] In some embodiments, the first type of aberration of the first aberration correction plate may be astigmatism. For example, in some embodiments, the amplitude of the first aberration correction plate may be based on the square root of the sum of the squares of the fifth Zernike term of astigmatism and the sixth Zernike term of astigmatism, which may be based on the determined wavefront aberration of the optical system. As a result, the first aberration correction plate may be configured to at least partially correct both the fifth Zernike term and the sixth Zernike term when disposed on the pupil plane of the optical system and rotated to align with the direction of the first type of aberration of the optical system.

[0038] In some embodiments, the second type of aberration of the second aberration correction plate may be coma. For example, in some embodiments, the amplitude of the second aberration correction plate may be based on the square root of the sum of the squares of the seventh Zernike term of coma and the eighth Zernike term of coma, which may be based on the determined wavefront aberration of the optical system. As a result, the second aberration correction plate may be configured to at least partially correct both the seventh Zernike term and the eighth Zernike term when disposed on the pupil plane of the optical system and rotated to align with the direction of the second type of aberration of the optical system.

[0039] In some embodiments, the optical system may be an imaging tool.

[0040] In some embodiments, the method may further include providing an apodization correction plate configured to at least partially correct apodization.

[0041] One or more embodiments of the present disclosure disclose an optical system with aberration correction. The system includes an illumination source. The system includes a detector. The system includes one or more condenser optical elements configured to image a sample onto the detector based on illumination from the illumination source. The system includes one or more aberration correction plates disposed on one or more pupil planes of the one or more condenser optical elements to perform at least partial correction of one or more linearly independent aberration terms, where any particular one of the one or more aberration correction plates has a spatially varying thickness profile and provides a selected amount of correction for a single particular aberration term of the one or more linearly independent aberration terms. The one or more aberration correction plates include a first aberration correction plate configured to at least partially correct a first aberration term characterizing a first type of aberration, where the first type of aberration is any one of spherical aberration, coma aberration, or trefoil aberration, and where any aberration correction plate including an aberration term characterizing the aberration type of spherical aberration, coma aberration, or trefoil aberration is configured to be rotated to align with the direction of the aberration type of the optical system.

[0042] According to one or more embodiments of the present disclosure, a system with aberration correction is disclosed. The system includes an illumination source. The system includes a detector. The system includes one or more condenser optical elements configured to image a sample onto the detector based on illumination from the illumination source. The system includes a catalog of aberration correction plates. The catalog includes one or more sets. Each set of the one or more sets includes one or more aberration correction plates that provide at least partial correction of specific linearly independent aberration terms. Any particular one of the one or more aberration correction plates has a spatially varying thickness profile that provides a selected amount of correction for a specific linearly independent aberration term among the one or more linearly independent aberration terms. Each set corrects different specific linearly independent aberration terms. Each specific linearly independent aberration term characterizes a type of aberration among one or more types of aberration, where each type of aberration among the one or more types of aberration is one of spherical aberration, coma aberration, or trefoil aberration. The optical system includes a selected combination of one or more aberration correction plates that at least partially corrects aberration within a selected tolerance. Each aberration correction plate of the selected combination is one of the aberration correction plates of one of the one or more sets, where an aberration correction plate including an aberration term characterizing the aberration type of spherical aberration, coma aberration, or trefoil aberration is configured to be rotated to align with the direction of the aberration type of the optical system.

[0043] One or more embodiments of the present disclosure disclose a method for correcting aberrations of an optical system. The method includes determining the wavefront aberration of the optical system. The method includes providing one or more aberration correction plates for the optical system. Each of the one or more aberration correction plates is configured to at least partially correct one of the one or more aberration terms. Each of the one or more aberration terms is linearly independent of each other and is configured to characterize the type of aberration, and each aberration term characterizes the type of aberration of the optical system and is based on the determined wavefront aberration. The one or more aberration correction plates include a first aberration correction plate configured to at least partially correct a first aberration term. The first aberration term characterizes a first type of aberration, where the first type of aberration is one of spherical aberration, coma aberration, or trefoil aberration, and any aberration correction plate including an aberration term characterizing the aberration type of spherical aberration, coma aberration, or trefoil aberration is configured to be rotated to align with the direction of the aberration type of the optical system.

[0044] It should be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not necessarily limiting of the claimed invention. The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and, together with the general description, serve to explain the principles of the invention.

Brief Description of the Drawings

[0045] Many advantages of the present disclosure will be better understood by those skilled in the art by referring to the accompanying drawings.

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Figure 5B

DETAILED DESCRIPTION OF THE INVENTION

[0046] The present disclosure specifically shows and describes specific embodiments and their specific features. The embodiments described herein are considered to be illustrative rather than limiting. It will be readily apparent to those skilled in the art that various changes and modifications in form and detail can be made without departing from the spirit and scope of the present disclosure. The subject matter disclosed herein is referred to in detail and is shown in the accompanying drawings.

[0047] Referring generally to FIGS. 1-5B, systems and methods for correcting aberrations and / or apodization of an optical system are disclosed in accordance with one or more embodiments of the present disclosure. Embodiments of the present disclosure relate to providing one or more aberration and / or apodization correction plates configured to at least partially correct wavefront aberrations and / or apodization of an optical system, where each aberration correction plate corrects a different aberration term. Further embodiments of the present disclosure relate to one or more aberration correction plates, where each plate provides a selected amount of correction for a single aberration type. Further embodiments relate to an optical system including first and second aberration correction plates, where the first and second aberration correction plates correct different aberration terms characterizing different aberration types of the optical system.

[0048] Further embodiments relate to a system for correcting aberrations of an optical system, including a catalog of aberration and / or apodization correction plates that can be used to flexibly adjust aberration and / or apodization correction of the optical system. For example, some embodiments of the present disclosure relate to a system including a catalog having one or more sets of two or more aberration correction plates (optionally, also capable of correcting apodization alone), where each set is associated with an aberration term (e.g., spherical aberration, coma aberration, etc.) and corrects a range of values of that aberration term (e.g., a first plate for correcting 20 milliwave (mWave) values of spherical aberration, a second plate for correcting 40 mWave of spherical aberration, etc.).

[0049] Wavefront measurement and control are generally important considerations for high-resolution optical systems operating near the diffraction limit. The presence of unwanted optical aberrations in an optical system causes image distortion, reduced image contrast, and stray light losses. Thus, optical aberrations are closely related to system performance and the quality of the optical system.

[0050] In general, a circular wavefront aberration profile can be mathematically modeled using Zernike polynomials. Zernike polynomials are orthogonal on a circle with a unit radius. A complex wavefront aberration is fitted with Zernike polynomials to obtain a set of fitting coefficients, and each coefficient in the set represents a different linearly independent type of aberration. Thus, each Zernike term (i.e., each coefficient multiplied by the Zernike polynomial) can quantify the type of aberration contributing to the overall wavefront aberration individually and separately. Note that both even and odd Zernike polynomials can exist.

[0051] Note that there may be cases where multiple aberrations in an optical system can be corrected using a single element. For example, correcting multiple aberrations using a single aberration correction plate is generally described in U.S. Patent No. 10,761,031 entitled "ARBITRARY WAVEFRONT COMPENSATOR FOR DEEP ULTRAVIOLET (DUV) OPTICAL IMAGING SYSTEM", the entire content of which is incorporated herein by reference. In another example, simultaneous correction of focus (Z4) and astigmatism (Z5 and Z6) using a dependent combination of at least two plates is generally described in U.S. Patent No. 5,966,243 entitled "PROCESS FOR CORRECTING WAVE FRONT DEFORMATIONS" issued on October 12, 1999, the entire content of which is incorporated herein by reference. However, it is contemplated that this approach may have limitations herein. For example, a single aberration correction plate for correcting various types of aberrations (e.g., coma aberration, astigmatism, etc.) in an optical system can be essentially customized to that system. It may not be practical to provide a set of single aberration correction plates that can each simultaneously correct for all possible combinations of all possible values of each type of aberration. Thus, a single aberration correction plate for simultaneously correcting various types of aberrations may essentially be tied to the particular individual optical system for which it is designed. Any change to the optical system can potentially change the wavefront aberration of the optical system, which may require another aberration correction plate, increasing costs and potentially causing significant delays. For example, as the aberration tolerance requirements become more stringent, the production costs and lead times for critical components such as high numerical aperture (NA) objective lenses may increase. Further, if the optical aberrations of the objective lens exceed the tolerance requirements, replacing components to reduce the aberrations can be costly and potentially cause significant delays.

[0052] Some embodiments relate to systems and methods for correcting aberrations of an optical system that address at least some of these concerns. For example, in some applications, it may be possible to provide an optical system that can generate an aberration-corrected image using one or more aberration correction plates. In this example, the change in wavefront aberration of the optical system can be at least partially corrected using one or more correction plates, and the correction plates may not need to be specifically designed for the optical system. For example, the wavefront aberration of the optical system can be at least partially corrected by using one or more aberration correction plates, and each aberration correction plate corrects different linearly independent aberration terms of the wavefront aberration.

[0053] In this regard, or as another example, a catalog of aberration correction plates may be used, which includes at least one set of correction plates that correct different amounts of specific aberration terms. As an example, the catalog can include a set of aberration correction plates to correct spherical aberration, and each plate provides a different correction amount (e.g., 5 mWave, 10 mWave, 15 mWave, etc.). In this way, the spherical aberration in a specific optical system can be corrected within the selected tolerance by utilizing (or selecting) the plate that provides the required correction amount. Further, the catalog can include multiple (e.g., two or more) sets of correction plates, and each set corrects different aberration terms. Thus, complex aberrations in an optical system can be corrected within the selected tolerance by utilizing (or selecting) multiple plates from different sets.

[0054] It should be noted that apodization is a change in the transmission of light across the pupil. A highly uniform pupil transmission corresponds to a small apodization. Small apodization is desirable for high NA systems because large apodization reduces the effective NA of the system. It should be noted that the apodization (i.e., pupil transmission) of a high NA optical system can exhibit higher transmission near the pupil center than near the pupil edge of the optical system.

[0055] At least some embodiments of the present disclosure include an apodization correction plate, which may be an aberration correction plate with apodization correction.

[0056] Regarding apodization, in at least some embodiments, as further described in the following optional steps, at least one aberration correction plate (e.g., 118a) in the catalog of aberration correction plates may have an apodization coating on at least one surface of the aberration correction plate. For example, the apodization coating may be configured to at least partially correct the non-uniformity of the pupil transmission of the optical system.

[0057] For example, each aberration correction plate of the set can at least partially correct a specific value within a range of values of a specific aberration term, and the set can cover a range of values of the specific aberration term. For example, a change in the optical system can cause a change in the wavefront aberration of the optical system. Further, with respect to this example, the wavefront aberration can be at least partially corrected by replacing an existing aberration correction plate of an optical system having a specific value of a specific aberration term with a selected aberration correction plate having a different value of the same aberration term. In another embodiment of this example, the selected aberration correction plate can be used without replacing the existing aberration correction plate. Further, with respect to this example, the selected aberration correction plate may already be in stock and / or may be mass-produced, and thus the cost of such an aberration correction plate is relatively low and the lead time is relatively short. Due to the advantages of such a system or method, in at least some embodiments, it is at least possible to have a catalog of aberration correction plates covering one or more aberration types (e.g., coma aberration, astigmatism, spherical aberration, etc.) (or purchase one or more aberration correction plates in a relatively short time) so that the aberration correction plate of the optical system can be quickly replaced (or added) in response to a change in the wavefront aberration of the optical system. Further, such systems and methods can at least possibly reduce the cost of correcting the aberrations of an optical system in some embodiments, which is because such aberration correction plates can be used in multiple systems and mass-produced, and / or because they are easier to manufacture than a single plate that corrects various aberration terms.

[0058] At least some embodiments of the present disclosure include an aberration correction plate that can be used in an optical system (e.g., insertable into a pupil plane). For example, the aberration correction plate can be a thin transparent plate having a varying two-dimensional (2D) thickness configured to be used at or near the pupil plane of an optical system (e.g., an imaging system). For example, the 2D thickness can be changed by ion beam figuring (IBF) technology or other profile-defining techniques or methods such that the transmitted wavefront profile from the aberration correction plate cancels (e.g., corrects) at least a portion of the aberration of the optical system when the orientation of the plate (i.e., rotation about the optical axis of the optical system) is correct or nearly correct. In this regard, the aberration correction plate can spatially modify the optical path across the pupil to cancel (e.g., compensate for) wavefront aberration.

[0059] Furthermore, note that an optical system with aberration correction can be utilized in a wide range of applications. Thus, the spirit and scope of the present disclosure are not limited to high NA or high-resolution measurement systems and can be extended to any application of an optical system with one or more aberration correction plates.

[0060] FIG. 1A is a schematic representation of an optical system with aberration correction according to one or more embodiments of the present disclosure. In one embodiment, as shown in FIG. 1, the optical system 100 includes one or more aberration correction plates 110 (e.g., including a first aberration correction plate 110a, and optionally a second aberration correction plate 110b, up to an Nth aberration correction plate 110n), each of which can correct aberration terms. For example, as shown, the optical system 100 can include an imaging optical element 104 and can include any suitable number and type of imaging optical elements. As shown, the optical system can be configured to image an object 102 using electromagnetic waves (e.g., light from a light source) to form an image 106, and the electromagnetic waves can be reflected from the object 102 or transmitted through the object 102 (e.g., from a light source located behind the object 102) and can be represented by a plurality of wavefronts 108. Light can pass through any number and type of imaging optical elements 104. Each element of the imaging optical element 104 may introduce aberration into the system, whereby the wavefront may be distorted as shown by the distorted wavefront 112a compared to the ideal undistorted wavefront 112b. For example, element imperfections, or incorrect placement or orientation of the elements of the imaging optical element 104 can cause aberration and distort the wavefront 108. Further, the design of the optical system 100 itself may introduce aberration (e.g., even with a perfect imaging optical element 104, it may not be avoidable with a given set of design constraints). One or more aberration correction plates 110 can be used to compensate (i.e., correct) such a distorted wavefront 112a. The one or more aberration correction plates 110 can bring the distorted wavefront 112a closer to the ideal undistorted wavefront 112b, as shown by the partially corrected wavefront 112c. Some of the advantages of the at least partially corrected wavefront 112c can include being able to meet more stringent aberration tolerance requirements, being able to generate a sharper image, and / or being able to generate a more accurate and less degraded image of the object 102. Other advantages can include at least being able to correct residual wavefront errors caused by the manufacturing steps of the optical system.

[0061] Regarding apodization, in at least some embodiments, at least one of the aberration correction plates of the optical system 100 (e.g., 110a), as further described below in any step, may have an apodization coating on at least one surface of the aberration correction plate 110. For example, the apodization coating may be configured to at least partially correct the non-uniformity of the pupil transmission of the optical system 100. In another example, the apodization coating may be configured to have a lower transmittance (e.g., lower transmittance near the center (e.g., the optical axis) than at the edge). In another example, the apodization coating may be configured to vary the transmittance radially according to a radial variation function in which the transmittance increases from the center of the pupil.

[0062] FIG. 1B is a schematic representation of a catalog 114 of one or more sets 116 (e.g., a first set 116a, and optionally a second set 116b, up to an Nth set) of aberration correction plates (e.g., aberration correction plate 118a of the first set 116a, aberration correction plate 118b of the first set 116a, up to the Nth aberration correction plate of the first set 116a) configured to at least partially correct the wavefront aberration of an optical system (e.g., optical system 100 of FIG. 1A) according to one or more embodiments of the present disclosure. In one embodiment, each set 116 is configured to at least partially correct the aberration terms associated with each set. For example, each aberration term may be linearly independent from each of the other aberration terms and may be configured to characterize the type of aberration. For example, each aberration correction plate 118 of the first set 116a may be configured to at least partially correct the aberration terms associated with and characterizing spherical aberration, and each aberration correction plate 120 of the second set 116b may be configured to at least partially correct the aberration terms associated with and characterizing coma aberration. In this regard, the first aberration correction plate 118a of the first set 116a can correct spherical aberration with a value of 20 mWave, the second plate 118b can correct spherical aberration with a value of 40 mWave, and this pattern can continue for the other aberration correction plates 118 of the first set 116a. Similarly, the range of values of coma aberration can be corrected by the aberration correction plates 120 of the second set 116b. It should be noted that the above examples are provided for illustrative purposes only, and the sets can be associated with any aberration terms and any aberration types. For example, the fact that other examples of aberration terms and aberration types are not included may simply be for the sake of brevity. For example, catalog 114 may include sets 116a associated with linearly independent aberration terms or aberration types. In another example, catalog 114 may include sets 116a associated with any Zernike terms.

[0063] In another embodiment, at least one (e.g., 118a) of the aberration correction plates in catalog 114 can be configured to be used in an optical system (e.g., optical system 100 of FIG. 1, or imaging tool 122 of FIG. 1C detailed below). For example, aberration correction plate 118a can be configured to be inserted into optical system 100. In another example, aberration correction plate 118a can be configured to be inserted into one or more pupil planes of optical system 100. In another example, aberration correction plates 110 (e.g., one aberration correction plate 110 from each set) from one or more of the one or more sets 116 can be selected for, utilized by, or inserted into optical system 100. For example, aberration correction plate 118 may be selected from the first set 116a, which may be aberration correction plate 110a shown in FIG. 1A. Further, with respect to this example, aberration correction plate 120 is selected from the second set 116b and may be aberration correction plate 110b. In this regard, if the first set 116a at least partially corrects spherical aberration and the second set 116b at least partially corrects coma aberration, then by combining and using the aberration correction plates 110 from each set 116, both spherical aberration and coma aberration are at least partially corrected.

[0064] Referring again to FIG. 1B, a system for correcting the aberration of an optical system is disclosed. For example, the system can include a catalog. For example, the catalog can include one or more sets. In this regard, a set may include a plurality (e.g., two or more) of aberration correction plates. For example, each of the plurality of aberration correction plates of a set can be configured to at least partially correct a preset range of catalog values of aberration terms associated with that set. For example, each aberration term can be configured to be linearly independent of each other and to characterize the type of aberration (e.g., spherical aberration, coma aberration, spherical aberration, etc.).

[0065] There may be catalogs for the astigmatism set of the aberration correction plate, the coma aberration set of the aberration correction plate, and the spherical aberration set of the aberration correction plate. Further, the astigmatism set of the aberration correction plate may include a first aberration correction plate of 20 mWave, a second aberration correction plate of 40 mWave, a third aberration correction plate of 60 mWave, and the like. Similarly, the coma aberration set of the aberration correction plate may include a first aberration correction plate of 10 mWave, a second aberration correction plate of 20 mWave, a third aberration correction plate of 30 mWave, and the like. Similarly, the spherical aberration set of the aberration correction plate may also span over a range of preset catalog values. Each set of aberration correction plates may be used in or selected for use in the optical system 100 and may be configured to at least partially correct the aberration type associated with each set. Further, if there is no aberration type or it is below a threshold (e.g., 5 mWave), the aberration correction plate from the set associated with such an aberration type may be determined not to be used in the optical system 100.

[0066] FIG. 1C is a conceptual diagram showing an imaging tool 122 according to one or more embodiments of the present disclosure. In one embodiment, the imaging tool 122 includes an illumination source 124 configured to generate at least one illumination beam 126. The illumination from the illumination source 124 may include one or more selected wavelengths of light, including but not limited to ultraviolet (UV) radiation, visible radiation, or infrared (IR) radiation. For example, the imaging tool 122 may include one or more apertures in the illumination pupil plane and may split the illumination from the illumination source 124 into one or more illumination beams 126 or illumination lobes. Note that the imaging tool 122 may provide dipole illumination, orthogonal phase illumination, and the like. Further, the spatial profile on the sample 128 of one or more illumination beams 126 may be controlled by the field stop and may have any selected spatial profile.

[0067] The illumination source 124 can include any type of illumination source suitable for providing at least one illumination beam 126. In one embodiment, the illumination source 124 is a laser source. For example, the illumination source 124 can include, but is not limited to, one or more narrowband laser sources, broadband laser sources, supercontinuum laser sources, white light laser sources, etc. In this regard, the illumination source 124 can provide an illumination beam 126 having high coherence (e.g., high spatial coherence and / or temporal coherence). In another embodiment, the illumination source 124 includes a laser sustained plasma (LSP) source. For example, the illumination source 124 can include, but is not limited to, an LSP lamp, an LSP bulb, or an LSP chamber, which are suitable for accommodating one or more elements that can emit broadband illumination when excited to a plasma state by a laser source. In another embodiment, the illumination source 124 includes a lamp source. For example, the illumination source 124 can include, but is not limited to, an arc lamp, a discharge lamp, an electrodeless lamp, etc. Note that the illumination source 124 can provide an illumination beam 126 having low coherence (e.g., low spatial coherence and / or temporal coherence). In another embodiment, the illumination source 124 includes a high-brightness illumination source formed from a plurality of coherent light sources into a single output distribution. For example, a high-brightness illumination source including a plurality of coherent light sources configured to provide a single output distribution in a common étendue is generally described in U.S. Patent Application No. 16,430,861, filed on June 4, 2019, the entire disclosure of which is incorporated herein by reference.

[0068] The illumination source 124 may provide an illumination beam 126 using free-space technology and / or optical fibers. In one embodiment, the illumination source 124 generates a multi-lobe illumination beam 126 by supplying light to two or more optical fibers, where the light output from each optical fiber is an illumination lobe of the illumination beam 126. In another embodiment, the illumination source 124 generates a multi-lobe illumination beam 126 by diffracting a light source into two or more diffraction orders, where the illumination lobes of the illumination beam 126 are formed from at least a portion of the diffraction orders of the light source. The efficient generation of multiple illumination lobes by controlled diffraction is generally described in U.S. Patent Application Publication No. US2020 / 0124408, published on March 14, 2019, entitled "Efficient Illumination Shaping for Scatterometry Overlay", which is hereby incorporated by reference in its entirety.

[0069] In another embodiment, the imaging tool 122 directs the illumination beam 126 to the sample 128 via an illumination path 130. The illumination path 130 may include one or more optical elements suitable for modifying and / or conditioning the illumination beam 126 and for directing the illumination beam 126 towards the sample 128. In one embodiment, the illumination path 130 includes one or more illumination path lenses 132 (e.g., for collimating the illumination beam 126, relaying the pupil and / or field plane, etc.). In another embodiment, the illumination path 130 includes one or more illumination path optical elements 134 for shaping or controlling the illumination beam 126. For example, the illumination path optical elements 134 may include, without limitation, one or more field stops, one or more pupil stops, one or more polarizers, one or more filters, one or more beam splitters, one or more diffusers, one or more homogenizers, one or more apodizers, one or more beam shapers, or one or more mirrors (e.g., stationary mirrors, translational mirrors, scanning mirrors, etc.).

[0070] In another embodiment, the imaging tool 122 includes an objective lens 136 and focuses the illumination beam 126 onto the sample 128 (e.g., a target having target elements located on two or more layers of the sample 128). In another embodiment, the sample 128 is disposed on a sample stage 138 suitable for fixing the sample 128 and is further configured to position the sample 128 relative to the illumination beam 126.

[0071] In another embodiment, the imaging tool 122 includes one or more detectors 140 configured to capture light or other things (e.g., the collected light 150) emitted from the sample 128 (e.g., a target on the sample 128) via a collection path 142. The collection path 142 may include one or more optical elements suitable for modifying and / or adjusting the collected light 150 from the sample 128. In one embodiment, the collection path 142 includes one or more collection path lenses 144 and may, but need not, include the objective lens 136 (e.g., for collimating the illumination beam 126, relaying the pupil and / or field plane, etc.). In another embodiment, the collection path 142 includes one or more collection path optical elements 146 for shaping or controlling the collected light 150. For example, the collection path optical elements 146 may include, but are not limited to, one or more field stops, one or more pupil stops, one or more polarizers, one or more filters, one or more beam splitters, one or more diffusers, one or more homogenizers, one or more apodizers, one or more beam shapers, or one or more mirrors (e.g., stationary mirrors, translational mirrors, scanning mirrors, etc.).

[0072] Detector 140 can be disposed at any selected position within collection path 142. In one embodiment, imaging tool 122 includes detector 140 in the field plane (e.g., the plane conjugate with sample 128) and generates an image of sample 128. In another embodiment, imaging tool 122 includes detector 140 in the pupil plane (e.g., the diffraction plane) and generates a pupil image. In this regard, the pupil image can correspond to the angular distribution of light from sample 128 to detector 140. For example, the diffraction order associated with the diffraction of illumination beam 126 from sample 128 (e.g., a target on sample 128) can be imaged or otherwise observed within the pupil plane. In a general sense, detector 140 can capture any combination of reflected (or transmitted) light, scattered light, or diffracted light from sample 128.

[0073] Imaging tool 122 can generally include any number or type of detector 140 suitable for capturing light from sample 128 that indicates an overlay. In one embodiment, detector 140 includes one or more detectors 140 suitable for characterizing a static sample. Here, imaging tool 122 can operate in a static mode where sample 128 is stationary during measurement. For example, detector 140 can include a two-dimensional pixel array, e.g., but not limited to, a charge-coupled device (CCD) or a complementary metal oxide semiconductor (CMOS) device. In this regard, detector 140 can generate a two-dimensional image (e.g., a field plane image or a pupil plane image) in a single measurement.

[0074] In one embodiment, detector 140 includes one or more detectors 140 suitable for characterizing a moving sample (e.g., a scanned sample). Still, imaging tool 122 can operate in a scanning mode where moving sample 128 is scanned relative to the measurement field of view during measurement. For example, detector 140 can include a two-dimensional pixel array having a capture time and / or a refresh rate sufficient to capture one or more images within a selected image tolerance (e.g., image blur, contrast, sharpness, etc.) during scanning. As another example, detector 140 can include a line scan detector and can continuously generate an image of one line of pixels at a time. As another example, detector 140 can include a time delay integration (TDI) detector.

[0075] In another embodiment, the imaging tool 122 includes a controller 152. The controller 152 can include one or more processors 154 configured to execute program instructions held on a storage medium 156 or memory. In this regard, one or more processors 154 of the controller 152 can execute any of the various process steps described throughout the present disclosure. Further, the controller 152 can be communicatively coupled to the imaging tool 122 or any component therein.

[0076] In another embodiment, the imaging tool 122 includes a scanning subsystem that scans the sample 128 across the measurement field of view during the measurement. For example, the sample stage 138 can place and orient the sample 128 within the focal volume of the objective lens 136. In another embodiment, the sample stage 138 includes one or more adjustable stages, such as, but not limited to, a linear translation stage, a rotational stage, or a tip / tilt stage. In another embodiment, although not shown, the scanning subsystem includes one or more beam scanning optics (e.g., a rotating mirror, a galvanometer, etc.) that scan the illumination beam 126 across the sample 128.

[0077] The illumination path 130 and the collection path 142 of the imaging tool 122 can be oriented in a wide range of configurations suitable for illuminating the sample 128 with the illumination beam 126 and collecting the light emitted from the sample 128 in response to the incident illumination beam 126. For example, as shown in FIG. 1B, the imaging tool 122 can include a beam splitter 148, and the beam splitter 148 is oriented such that a common objective lens 136 can direct the illumination beam 126 toward the sample 128 and collect the light from the sample 128 simultaneously. As another example, the illumination path 130 and the collection path 142 can include non-overlapping optical paths.

[0078] In one embodiment, the imaging tool 122 may include one or more aberration correction plates 110 (e.g., 118a and 120a in FIG. 1B, or 110a and 110b in FIG. 1A) for at least partially correcting aberration terms. For example, as described above, the one or more aberration correction plates 110 may be selected from the catalog 114.

[0079] In another embodiment, the one or more aberration correction plates 110 may be disposed on one or more pupil planes of the imaging tool 122 and may be configured to at least partially correct the aberration of the imaging tool 122. For example, the first aberration correction plate 110 may be configured to be used at the first pupil plane, and the second aberration correction plate 110 may be configured to be used at the second pupil plane. For example, the first aberration correction plate 110 and the second aberration correction plate 110 may be configured to be used at the first pupil plane. For example, the first aberration correction plate 110 and the second aberration correction plate 110 may be configured to be used adjacent to and on both sides of the pupil plane.

[0080] It is contemplated herein that the design of a particular optical system 100 may limit the thickness of the aberration correction plate 110 or the number of aberration correction plates 110 that can be disposed at or sufficiently close to a particular pupil plane to provide aberration correction within a selected tolerance. For example, the thickness of the aberration correction plate 110 may be relatively thin (e.g., 0.5 mm or less). For example, the thickness of the aberration correction plate 110 may be as thin as possible, and the thinness of the aberration correction plate 110 may be limited in part by the polishing process used to manufacture the aberration correction plate 110.

[0081] For the purposes of the present disclosure, a description showing the arrangement of one or more aberration correction plates within the pupil plane can be understood as the arrangement of one or more aberration correction plates within a distance range from the pupil plane that provides aberration correction within a selected tolerance. It should be noted that collimated light waves can enable the same amount of aberration correction within a selected tolerance within a distance range beyond the pupil plane (e.g., up to 15 cm or more). For example, an optical system equipped with a complex objective lens having a pupil plane within the objective lens (e.g., having many optical elements) may not be able to place an aberration correction plate within the objective lens for various reasons (i.e., there is not enough space). For example, the aberration correction plate may need to be placed outside the objective lens (e.g., 10 cm from / beyond the pupil plane). In this regard, when the aberration correction plate is arranged over a wide range, when a test object such as a reticle is placed on the front focal plane of the objective lens and the light waves passing through the objective lens are collimated by the objective lens, aberration correction may be possible within a selected tolerance. For the purposes of the present disclosure, in the expression "within a distance range from the pupil plane that provides aberration correction within a selected tolerance", the term "range" may vary depending on whether the light wave passes through the pupil plane and is collimated, and to what extent the light wave is collimated as it passes through the pupil plane.

[0082] For the purposes of the present disclosure, a description showing two or more correction plates (e.g., aberration correction plates) can be understood as one or more correction plates (e.g., aberration correction plates) when at least one of the aberration types of one or more of the correction plates is one of spherical aberration, coma aberration, or trefoil aberration. For example, a single coma aberration correction plate provided using the equations and other characteristics described below in relation to Z7 and Z8 may be referred to in relation to FIGS. 5A and 5B and may be provided instead of providing two or more aberration correction plates in method step 204. Further, for the purposes of the present disclosure, a description showing two or more sets of catalogs can be understood as one or more sets of catalogs when at least one of the aberration types of one or more of the correction plates in one or more of the sets is one of spherical aberration, coma aberration, or trefoil aberration.

[0083] Furthermore, the optical system can include any number of optical relays and provide any number of conjugate pupil planes where an aberration correction plate can be disposed. Thus, the description herein showing the placement of one or more aberration correction plates at the pupil plane can be understood to include any placement of aberration correction plates at any number of conjugate pupil planes.

[0084] FIG. 2 schematically illustrates a method for correcting aberrations of an optical system according to one or more embodiments of the present disclosure.

[0085] In step 202, the wavefront aberration of the optical system can be measured. For example, the wavefront of the optical system can be distorted by elements of the system's imaging optics or by the system's design, and such distortion can be measured. For example, referring to FIG. 1A, the imaging optic 104 can distort the wavefront 108 (see the distorted wavefront 112a). Further, in this case, the distorted wavefront 112a (i.e., the wavefront aberration) can be measured. For example, in an optical system in the ultraviolet to visible wavelength range, the aberration can be measured using a Shack-Hartmann sensor. In another example, in an EUV actinic system, the aberration can be determined using a phase-shifting point diffraction interferometer, and further described in "Extreme-ultraviolet phase-shifting point-diffraction interferometer: a wave-front metrology tool with subangstrom reference-wave accuracy" by Patrick P. Naulleau et al., Applied Optics, Vol. 38, No. 35, December 10, 1999, which is hereby incorporated by reference in its entirety. Additionally, several examples for determining aberrations in an EUV type system are further described in U.S. Patent No. 9,335,206 issued to Zhang et al. on May 10, 2016, which is hereby incorporated by reference in its entirety.

[0086] In the optional step, method 200 may include fitting the measured wavefront aberration to linearly independent aberration terms. For example, method 200 may include fitting the measured wavefront aberration 112b to linearly independent Zernike polynomials or terms.

[0087] In step 204, two or more aberration correction plates 110 (e.g., aberration correction plate 110a and aberration correction plate 110b) configured to at least partially correct two or more aberration terms may be provided. For example, a first aberration correction plate 110a configured to at least partially correct a first aberration term among the plurality of aberration terms may be provided. Further, each of the plurality of aberration terms may be linearly independent of each other and configured to characterize a type of aberration. For example, each of the plurality of aberration terms may be configured to characterize the type of aberration based on the measured wavefront aberration (e.g., 112a in FIG. 1A). Further, with respect to the above example, each aberration term of the two or more aberration terms may characterize a different type of aberration of the optical system 100.

[0088] In one example, the first type of aberration of the first aberration correction plate among the two or more aberration correction plates, and the second type of aberration of the second aberration correction plate among the two or more aberration correction plates may be one of astigmatism, coma aberration, spherical aberration, or trefoil aberration. In another example, the first type of aberration of the first aberration correction plate among the two or more aberration correction plates, and the second type of aberration of the second aberration correction plate among the two or more aberration correction plates may be one of any Zernike terms including higher-order Zernike terms.

[0089] One example of providing an aberration correction plate 110 (e.g., the first aberration plate 110a) may include correcting at least partially simultaneously on the same plate two Zernike terms when the Zernike terms are of the same aberration type. For example, the Zernike 5th term (Z5) and the Zernike 6th term (Z6) may be associated with spherical aberration, and there may be cases where it is desirable for the aberration correction plate 110 to correct spherical aberration. Any combination of Z5 and Z6 can be a wavefront of Z5 having an amplitude equal to the root sum square RSS of Z5 and Z6, but rotated by an angle determined by the Zernike coefficients of Z5 and Z6. This may similarly apply to the Zernike 7th and 8th terms (Z7 and Z8 respectively), and the Zernike 10th and 11th terms (Z10 and Z11 respectively). In this regard, such characteristics can be used to provide an aberration correction plate 110 that corrects two Zernike terms associated with the same type of aberration.

[0090] For example, in FIG. 3A, a spherical aberration wavefront 300 having a wavefront aberration type of Z5 spherical aberration is shown. The color of the spherical aberration wavefront 300 (e.g., the shade of gray used) corresponds to the wavefront aberration level, where medium gray (as shown in the corners) indicates that the aberration is zero. The spherical aberration correction plate 110 can be provided to correct (i.e., cancel out) such a spherical aberration wavefront 300 when the aberration correction plate 110 has a 2D thickness profile proportional to -w(x,y) / (n - 1) on a uniform substrate of constant thickness, where w(x,y) is the 2D wavefront phase function and n is the refractive index of the plate material. This can mean that the thickness decreases with positive phase (defined as a longer optical path length), and vice versa. These characteristics can also apply to other aberration terms (e.g., Z7 and Z8, and Z10 and Z11). When such a spherical aberration correction plate is provided, the Zernike 5th term (Z5) and the Zernike 6th term (Z6) projected in the XYZ coordinates can follow a sine function.

[0091]

Number

[0092] Here, θ is the rotation angle around the Z-axis in FIG. 3A, measured from 0 to π, and Z50 is the amplitude of the correction plate.

[0093] Examples of the above examples can be seen in FIGS. 4A and 4B. FIG. 4A shows a diagram of examples of Z5 402 and Z6 404. When the aberration correction plate is rotated as described above, projections of the sine waves Z5 402 and Z6 404 with respect to the rotation angle are generated. In this case, in the 2D plane having the horizontal axis Z5 and the vertical axis Z6, the coordinates of the system in FIGS. 4A and 4B are as follows. The measured system aberration Z5 is -32.7 mWave, and the measured Z6 is 12.48 mWave. Further, the RSS is 35 mWave, and the Z5 amplitude of the aberration correction plate is 35 mWave (indicated by the maximum height of Z5 402 in FIG. 4A). In this case, the azimuth angle φ (for example, within the range of 0 to 2π) is 159.09 degrees, and the projected Z5 and Z6 are 32.7 (indicated by point 406 of Z5) and -12.48 (indicated by point 408 of Z6), respectively (that is, these are opposite to the system aberration and the canceling system aberration). Generally, when the azimuth angle φ is in the range of 0 to π, the correction rotation angle (for example, the rotation angle of the aberration correction plate centered on the optical axis of the optical system) is θ = (φ + π) / 2, and when the azimuth angle φ is in the range of π to 2π, the correction rotation angle is θ = (φ - π) / 2. In this case, when the rotation angle of the aberration correction plate is rotated to (159.09 + 180) / 2 = 169.55 degrees (2.96 rad), the system aberrations Z5 and Z6 are completely corrected by the aberration correction plate with an amplitude of 35 mWave. This example shows that the system aberration can be corrected when, in at least some embodiments, the amplitude of the aberration correction plate 110 for Z5 is equal to the RSS of both the Z5 term and the Z6 term of the aberration (that is, the system aberration).

[0094] However, if the Z5 amplitude of the aspherical aberration correction plate is not the same as the RSS of the system aspherical aberration, there may be residual aspherical aberration, which is because the correction is not complete. Referring to FIG. 4B and the above examples, the system aspherical aberration RSS value is in the range of 10 to 100 mWave. It should be noted that the aspherical aberration correction plates in the library at 20 mWave intervals should theoretically not have an aspherical aberration correction plate exceeding 10 mWave from the ideal value. In this regard, FIG. 4B shows a simulation of the residual aspherical aberration RSS value after correction by an aspherical aberration correction plate with a 10 mWave and a 5-degree rotation angle error.

[0095] The residual aspherical aberration in FIG. 4B can be represented by the following function.

[0096]

Equation

[0097] Here, A s is the system aspherical aberration, φ s is the azimuth angle on the Z5Z6 plane, A c is the Z5 amplitude of the aspherical aberration correction plate, θ is the rotation angle, and Δ A is the RSS of the residual aspherical aberration after correction by the aspherical aberration correction plate. To theoretically correct the aspherical aberration completely, A c = A s and cos(2θ - φ s ) = -1 both hold. When A c ≠ A s , in some embodiments, the rotation angle θ that gives the minimum residual aspherical aberration satisfies the function cos(2θ - φ s ) = -1, and as a result, the second term in the above equation, 2A s A c (1 + cos(2θ - φ s )) is equal to zero.

[0098] Similar to the above examples and instances associated with the coma aberration (i.e., Z7 and Z8) and trefoil aberration (i.e., Z10 and Z11), the aberration correction plate 110 associated with the coma aberration can be provided similarly and / or can have similar characteristics. For example, in the case of coma aberration, the required rotation range is 0 to 2π. In the case of trefoil aberration, the required rotation range is 0 to (2 / 3)π. For example, using the RSS of Z7 and Z8, the amplitude of the aberration correction plate 110 associated with the coma aberration can be determined, and the angle of such an aberration correction plate 110 can be determined similarly based on the Zernike coefficients of the associated Zernike terms.

[0099] For example, similar to the examples described above for Z5 and Z6, providing an aberration correction plate for coma aberration can be similar to providing an aberration correction plate for the above-described astigmatism. For example, in the case of coma aberration, Z7 and Z8 projected in the XYZ coordinates can follow a sine function.

[0100]

Number

[0101] Here, θ is the rotation angle around the Z-axis in FIG. 3B, measured from 0 to 2π, and Z70 is the amplitude of the correction plate.

[0102] Examples of the above examples can be seen in FIGS. 5A and 5B. FIG. 5A shows a diagram of an example of Z7 502 and Z8 504. When the coma correction plate is rotated as described above, a projection of the sine wave with respect to the rotation angle of Z7 502 and Z8 504 is generated. In this case, in the 2D plane having the horizontal axis Z7 and the vertical axis Z8, the coordinates of the system in FIGS. 5A and 5B are as follows. The measured system coma Z7 is -27.46 mWave, and the measured Z8 is 21.7 mWave. Further, the RSS is 35 mWave, and the amplitude of Z7 of the coma correction plate is 35 mWave (indicated by the maximum height of Z7 502 in FIG. 5A). In this case, the azimuth angle φ (for example, within the range of 0 to 2π) is 141.68 degrees, and the projected Z7 and Z8 are 27.46 (indicated by point 606 of Z7) and -21.7 (indicated by point 508 of Z8), respectively (that is, these are opposite to the system coma and the canceling system coma). Generally, when the azimuth angle φ is in the range of 0 to π, the correction rotation angle (for example, the rotation angle of the coma correction plate centered on the optical axis of the optical system) is θ = φ + π, and when the azimuth angle φ is in the range of π to 2π, the correction rotation angle is θ = φ - π. In this case (FIG. 5A), when the rotation angle of the coma correction plate is rotated to 141.68 + 180 = 321.68 degrees (5.61 rad), the system coma Z7 and Z8 are completely corrected by the coma correction plate with an amplitude of 35 mWave. This example shows that the system coma can be corrected when, in at least some embodiments, the amplitude of the coma correction plate 110 with respect to Z7 is equal to the RSS of both the Z7 term and the Z8 term of the coma (that is, the system coma).

[0103] However, if the Z7 amplitude of the coma corrector plate is not the same as the RSS of the system coma, there may be residual coma, which is because the correction is not complete. Referring to FIG. 5B and the above examples, the system coma RSS value is in the range of 10 to 100 mWave. It should be noted that the coma corrector plates in the library at 20 mWave intervals should not theoretically have coma corrector plates exceeding 10 mWave from the ideal value. In this regard, FIG. 5B shows a simulation of the residual coma RSS value after correction by a coma corrector plate having a 10 mWave and a 5-degree rotation angle error.

[0104] The residual coma in FIG. 5B can be represented by the following function.

[0105]

Equation

[0106] Here, C s is the system coma, ψ s is the azimuth angle of the Z7Z8 plane, C c is the Z7 amplitude of the coma corrector plate, θ is the rotation angle, and Δ C is the RSS of the residual coma after correction. To theoretically correct the coma completely, C c = C s and cos(θ - ψ s ) = -1 both hold. When C c ≠ C s , in some embodiments, the rotation angle θ that gives the minimum residual coma satisfies the function cos(θ - ψ s ) = -1, and as a result, the second term in the above equation, 2C s C c (1 + cos(θ - ψ s )) is equal to zero.

[0107] In another example, in the case of trefoil aberration, Z10 and Z11 projected in the XYZ coordinates may follow a sine function.

[0108]

Equation

[0109] Here, θ is the rotation angle around the Z-axis, measured from 0 to (2 / 3)π, and Z100 is the amplitude of the correction plate.

[0110] By using quartz materials and IBF technology, the purity of the Zernike terms of the thin (e.g., 0.5 mm thick) Z5 aberration correction plate 110 can be very high. The amplitudes of other Zernike terms can be as small as about 1 mWave.

[0111] In FIG. 3B, a coma aberration wavefront 302 having a wavefront aberration type of coma aberration of Z9 is shown for illustrative purposes.

[0112] By using quartz or fused silica materials and IBF technology, the Zernike term purity of the thin (e.g., 0.5 mm thick) Z7 aberration correction plate 110 can be very high. The amplitudes of other Zernike terms can be as small as about 1 mWave.

[0113] In FIG. 3C, a spherical aberration wavefront 304 having a wavefront aberration type of spherical aberration of Zernike term 9 (Z9), which may be rotationally symmetric, is shown for illustrative purposes. For example, in the case of a Z9 aberration correction plate 110 for correcting spherical aberration, there is no need to rotate the plate.

[0114] In any step (not shown), at least one of the two or more aberration correction plates may be configured to correct apodization. For example, one or more aberration correction plates 110 of the optical system or imaging tool 122 may be aberration correction plates 110 configured to correct apodization (e.g., non-uniform pupil intensity distribution). For example, the aberration correction plate 110 (e.g., the aberration correction plate 110a in FIG. 1A) may be configured to correct apodization using a coating (on at least one of the first surface (not shown) or the second surface (not shown) of the aberration correction plate 110) that can improve the uniformity of the pupil transmission of the optical system. In this regard, the coating of the aberration correction plate may be configured to reduce the pupil transmission by an amount (e.g., 10% lower) near the center of the aberration correction plate. In another example, each aberration correction plate of the optical system 100 (e.g., imaging tool 122) may have a coating that corrects apodization (i.e., an apodization coating). The advantage of one or more correction plates that correct both apodization and aberration is an optical system that corrects both apodization and aberration. In another example, the apodization coating may be rotationally symmetric. It should be noted that the apodization described in the above examples and instances is for illustrative purposes only.

[0115] Apodization is not the same as aberration, but it should be noted that in at least some embodiments, any of the aberration correction plates mentioned may rather be an apodization correction plate. For example, any aberration correction plate may be an apodization plate that corrects apodization but does not correct any aberration terms. For example, the aberration correction plate 110a in FIG. 1A or the aberration correction plate 118a in FIG. 1B may be an apodization correction plate that corrects apodization but does not correct any aberration terms. In another example, the catalog 114 of aberration correction plates may be a catalog of aberration and apodization correction plates, or a catalog of apodization correction plates only. In this regard, the set 116a may be a set of aberration correction plates 118, and the set 116b may be a set of apodization correction plates, where the set 116a corrects aberration terms and the set 116b corrects a range of apodization values. From another perspective, or in addition to the above perspective, any aberration correction plate may be an aberration and apodization correction plate that corrects both apodization and aberration. For example, the set 116a may be a set of aberration and apodization correction plates 118.

[0116] Returning to FIG. 2 and referring thereto, at any step 206, two or more aberration correction plates may be inserted into the optical system. For example, referring to FIG. 1A, the first aberration correction plate 110a and the second aberration correction plate 110b may be two or more aberration correction plates and may be inserted into the optical system 100 or the imaging tool 122. For example, the first aberration correction plate 110a and the second aberration correction plate 110b may be inserted into a pupil plane (not shown) of the system 100. In this regard, the optical system 100 may have one or more pupil planes, and one or more aberration correction plates 110 may be inserted into one or more pupil planes of the optical system 100. For example, one or two of the two or more aberration correction plates 110 may be inserted into each pupil plane. In another example, each of all the aberration correction plates 110 is inserted into a different pupil plane of the optical system 100. For example, an aberration correction plate 110 that is not rotationally symmetric (which may include an aberration correction plate associated with astigmatism or coma) may be inserted into the optical axis of the optical system 100 at a rotation angle configured to at least partially correct the aberration terms associated with such an aberration correction plate 110. In another example, an aberration correction plate 110 that is rotationally symmetric (which may include an aberration correction plate associated with spherical aberration) may be inserted into the optical axis of the optical system 100 at any rotation angle with respect to the optical axis.

[0117] All methods described herein may include storing the results of one or more steps of a method embodiment in a memory. The results may include any result described herein and may be stored by any method well known in the art. The memory may include any memory described herein (e.g., memory 156), or any other suitable storage medium well known in the art. After the results are stored, the results are accessed in the memory and used by any of the method or system embodiments described herein, formatted for display to a user, and may be used by another software module, method, or system, etc. Further, the results may be stored "permanently," "semi-permanently," "temporarily," or for a period of time. For example, the memory may be a random access memory (RAM), and the results need not necessarily persist indefinitely in the memory.

[0118] It is further intended that each of the embodiments of the methods described above may include any other step(s) of any other method(s) described herein. Additionally, each of the embodiments of the methods described above may be performed by any of the systems described herein (e.g., the controller 152 of the imaging tool 122).

[0119] Those skilled in the art will recognize that the components, operations, devices, objects, and accompanying descriptions described herein are used as examples for clarity of concepts, and that modifications of various configurations are contemplated. Accordingly, as used herein, the specific examples and accompanying discussions described are intended to represent their more general classifications. In general, the use of a particular example is intended to represent that classification and should not be construed as limiting the exclusion of particular components, operations, devices, and objects.

[0120] As used herein, directional terms such as "top," "bottom," "front," "rear," "over," "under," "upper," "upward," "lower," "down," and "downward" are intended to provide relative positions for purposes of explanation and are not intended to specify an absolute reference frame. Various modifications to the described embodiments will be apparent to those skilled in the art, and the general principles defined herein may be applied to other embodiments.

[0121] Regarding the use of substantially any plural and / or singular terms herein, those skilled in the art may interpret from plural to singular and / or from singular to plural as appropriate to the context and / or application. Various permutations of singular / plural are not explicitly described herein for clarity.

[0122] The subject matter described in this specification may show different components contained within or connected to other components. It should be understood that such described architectures are merely exemplary, and in fact, many other architectures that achieve the same functionality may be implemented. In a conceptual sense, any arrangement of components for achieving the same functionality is effectively "associated" such that the desired functionality is achieved. Thus, any two components of this specification combined to achieve a particular functionality can be regarded as "associated" with each other, and as a result, the desired functionality is achieved regardless of the architecture or intermediate components. Similarly, any two components so associated can also be regarded as "connected" or "coupled" to each other to achieve the desired functionality, and any two components that may be so associated are regarded as "couplable" to each other to achieve the desired functionality. Particular examples of couplable include, but are not limited to, components that are physically mating and / or physically interacting, and / or wirelessly interacting and / or wirelessly interacting, and / or logically interacting and / or logically interactable components.

[0123] Furthermore, it should be understood that the present invention is defined by the appended claims. In general, it will be understood by those skilled in the art that the terms used herein, particularly in the appended claims (e.g., the body of the appended claims), are generally intended to be open terms (e.g., the term "including" should be construed as "including but not limited to", the term "having" should be construed as "having at least", the term "includes" should be construed as "includes but is not limited to", etc.). Where a specific number of introduced claim recitations is intended, such intent will be expressly recited in the claims, and it will be further understood by those skilled in the art that where such recitation is not present, such intent does not exist. For example, for purposes of illustration, the following appended claims may introduce claim recitations with the use of introductory phrases "at least one" and "one or more". However, the use of such phrases should not be construed to mean that the introduction of a claim recitation by the indefinite article "a" or "an" limits any particular claim scope that includes the claim recitation so introduced to an invention that includes only one such recitation, even if the same claim includes both the introductory phrase "one or more" or "at least one" and the indefinite article "a" or "an" (e.g., "a" and / or "an" should generally be construed to mean "at least one" or "one or more"), and the same holds true for the use of the definite article used to introduce a claim recitation. Additionally, even where a specific number of introduced claim recitations is expressly recited, those skilled in the art will recognize that such recitation should generally be construed to mean at least the recited number (e.g., a recitation of only "two recitations" without other modifiers generally means at least two recitations, or two or more recitations).Furthermore, in examples where conventional terms similar to "at least one of A, B, and C, etc." are used, generally, such a configuration is intended to have the meaning that a person skilled in the art would understand such a conventional term (for example, "a system having at least one of A, B, and C" includes, but is not limited to, a system having only A, only B, only C, A and B together, A and C together, B and C together, and / or A, B, and C together, etc.). In examples where conventional terms similar to "at least one of A, B, or C, etc." are used, generally, such a configuration is intended to have the meaning that a person skilled in the art would understand such a conventional term (for example, "a system having at least one of A, B, or C" includes, but is not limited to, a system having only A, only B, only C, A and B together, A and C together, B and C together, and / or A, B, and C together, etc.). It will be further understood by those skilled in the art that any substantially disjunctive and / or phrase representing two or more alternative terms should be understood to contemplate the possibility of including one of the terms, any of the terms, or both terms in the description, claims, or drawings. For example, the phrase "A or B" would be understood to include the possibility of "A" or "B" or "A and B".

[0124] Many of the features of the present disclosure and its attendant advantages will be understood from the foregoing description, and it will be apparent that various changes in the form, structure, and arrangement of the components can be made without departing from the disclosed subject matter or sacrificing all of its important advantages. The form described is merely illustrative, and the intent of the following claims is to embrace and include such changes. Further, it is to be understood that the invention is defined by the appended claims.

Claims

1. An optical system having aberration correction, comprising: a light source, a detector, one or more condenser optical elements configured to image a sample onto the detector based on illumination from the light source, and two or more aberration correction plates located at one or more pupil planes of the one or more condenser optical elements, providing at least partial correction of two or more linearly independent aberration terms in a Zernike polynomial representing wavefront aberration, wherein any particular one of the two or more aberration correction plates has a spatially varying thickness profile and provides a selected amount of correction for a single particular aberration term among the two or more linearly independent aberration terms; and at least one apodization correction plate configured to at least partially correct apodization; An optical system comprising the above.

2. The optical system according to claim 1, wherein at least one of the two or more aberration correction plates is configured to at least partially correct apodization.

3. The optical system according to claim 2, wherein at least one of the two or more aberration correction plates is configured to at least partially correct apodization, which is because at least one of the two or more aberration correction plates is an apodization coating configured to vary the transmittance radially according to a radial variation function in which the transmittance from the center of the pupil of the optical system increases with respect to the outer edge of the pupil when at least one of the aberration correction plates is disposed at the pupil plane of the optical system.

4. The two or more aberration correction plates include a first aberration correction plate configured to at least partially correct a first aberration term characterizing a first type of aberration, and a second aberration correction plate configured to at least partially correct a second aberration term characterizing a second type of aberration, wherein at least one of the first type of aberration or the second type of aberration is one of astigmatism, coma, spherical aberration, or trefoil aberration.

5. The two or more aberration correction plates further include a third aberration correction plate configured to at least partially correct a third aberration term of the two or more linearly independent aberration terms, where the third aberration term can characterize a third type of aberration of the optical system, and where the third type of aberration, the second type of aberration, and the first type of aberration are different, the optical system according to claim 4.

6. The optical system according to claim 5, wherein the third type of aberration is spherical aberration.

7. The first aberration correction plate is configured to at least partially correct the first aberration term when the first aberration correction plate is located on the one or more pupil planes of the optical system, and the second aberration correction plate is configured to at least partially correct the second aberration term when the second aberration correction plate is located on the one or more pupil planes of the optical system, the optical system according to claim 4.

8. The first aberration correction plate is configured to at least partially correct the first aberration term when the first aberration correction plate is located on a first pupil plane of the one or more pupil planes, and the second aberration correction plate is configured to at least partially correct the second aberration term when the second aberration correction plate is located on a second pupil plane different from the first pupil plane of the one or more pupil planes, the optical system according to claim 4.

9. Each of the two or more linearly independent aberration terms is a lower-order Zernike term within a span including Zernike terms 5 to 9, the optical system according to claim 1.

10. The optical system according to claim 1, wherein the optical system is an imaging tool.

11. Any aberration correction plate including an aberration term characterizing an aberration type of astigmatism, coma aberration, or trefoil aberration is configured to be rotated to align with the orientation of the aberration type within the optical system, the optical system according to claim 1.

12. Any aberration correction plate located on one or more pupil planes is disposed within a distance range from the one or more pupil planes, where the distance range is configured to perform aberration correction within a selected tolerance, the optical system according to claim 1.

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