Reflective objective

Abstract

All-reflective objective lens devices and methods designing such devices are described. The objective lens configurations include one or more freeform surfaces that and have high numerical apertures. An example all-reflective objective lens configuration includes at least four mirrors, where each mirror has a freeform surface, and is positioned to allow light from an object to enter objective lens configuration and reflect from each of the at least four mirrors only once before reaching a location of an aperture stop identifying an exit location objective lens configuration. The mirrors are positioned within the objective lens configuration to provide an unobscured field of view, a local optical axis of each of the mirrors is not colinear with a global optical axis of the all-reflective objective lens configuration, and the aperture stop is not positioned internal to the all-reflective objective lens configuration.

Description

REFLECTIVE OBJECTIVESTATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

[0001] This invention was made with government support under Grant No. 2034210 awarded by the National Science Foundation (NSF). The government has certain rights in the invention.CROSS-REFERENCE TO RELATED APPLICATION(S)

[0002] This application claims priority to the provisional application with serial number 63 / 519,749, titled “REFLECTIVE OBJECTIVE,” filed August 15, 2023. The entire contents of the above noted provisional application are incorporated by reference as part of the disclosure of this document.TECHNICAL FIELD

[0003] The disclosed technology relates to improved all-reflective objective lens configurations and methods associated with designing such configurations.

[0004] BACKGROUND

[0005] Reflective surfaces are used in biological microscopy to mitigate some of the problems associated with refractive components. Microscopes based on refractive optics are typically constrained to specific wavelength ranges, so multiple instruments are often required to investigate specimens over a broad spectrum (e.g., from the ultraviolet (UV) to infrared (IR) bands). Dispersion and spectrally dependent absorbance are two undesirable properties of optical materials that are largely responsible for this. While some reflective systems have been proposed to overcome these limitations, they include limitations that make those systems inefficient, cost prohibitive or ineffective for many applications.SUMMARY

[0006] The disclosed embodiments, among other features and benefits, describe all-reflective objective lens configurations that include one or more freeform surfaces that provide configurations with a high NA which are more efficient than standard approaches.

[0007] An example all-reflective objective lens configuration includes at least four mirrors, wherein each of the at least four mirrors includes a freeform surface, and each of the at least four mirrors is positioned within the all-reflective objective lens configuration to allow light from an object to enter the all-reflective objective lens configuration and reflect from each of the at least four mirrors only once before reaching a location of an aperture stop identifying an exit location of the all-reflective objective lens configuration. In the all-reflective objective lens configuration, the at least four mirrors are positioned within the all-reflective objective lens configuration to provide an unobscured field of view, a local optical axis of each of the at least four mirrors is not colinear with a global optical axis of the all-reflective objective lens configuration, and the aperture stop is not positioned internal to the all-reflective objective lens configuration.

[0008] BRIEF DESCRIPTION OF THE DRAWINGS

[0009] FIG. 1 Illustrates a four-mirror unobscured objective lens configuration in accordance with an example embodiment.

[0010] FIG. 2 Illustrates a four-mirror objective lens configuration in accordance with another example embodiment.

[0011] FIG. 3 Illustrates a configuration of an objective in accordance with another example embodiment.

[0012] FIG. 4 illustrates a prior art lens configuration.

[0013] FIG. 5 illustrates the local optical axes of the mirrors and a location of aperture stop associated with the configurations of FIG. 2.

[0014] FIG. 6 illustrates example modulation transfer function (MTF) plots associates with rotationally symmetric using prior designs and freeform designs in accordance with example embodiments.

[0015] FIG. 7 illustrates a starting configuration of a four-mirror objective lens system in accordance with a design process in accordance with an example embodiment.

[0016] FIG. 8 illustrates four example configurations with increasing numerical aperture values that are designed in accordance with example embodiments.

[0017] FIG. 9 illustrates a set of operations that can be performed for producing an all-reflective objective lens configuration in accordance with an example embodiment.DETAILED DESCRIPTION

[0018]

[0019] Dispersion occurs at boundaries between media with different refractive indices and can result in performance variation as a function of wavelength. For example, chromatic change of focus and chromatic change of magnification will both tend to degrade image quality in broad spectrum systems. Refractive systems are therefore typically specified for a finite wavelength range wherein reasonable chromatic aberration correction is possible. Electromagnetic waves reflecting from a mirror do not experience a change in ambient refractive index magnitude, so there will be no chromatic aberration in an all-reflective system. Additionally, while optical materials used for lens fabrication have a spectrally dependent absorbance that further limits their application over broad wavelength ranges, typical mirror substrate materials maintain high reflectance from the UV to IR.

[0020] An additional consideration for advanced microscopy techniques is the propagation of laser pulses through the system for illumination (e.g., for multiphoton microscopy); femtosecond lasers are common sources for this task. Temporally narrow pulses provide higher excitation efficiency of multiphoton phenomena, such as two- photon induced fluorescence and second-harmonic generation. Each pulse has a finite spectral bandwidth that is small compared to light emitting diodes (LEDs), but which is non-negligible. In a single pulse, the wavelength dependent refractive index of optical materials causes electromagnetic waves of different frequencies to arrive at the sample at different times, a phenomenon known as group delay dispersion (GDD). This broadens the pulse temporally, and therefore the refractive system's dispersion properties must be characterized and compensated for by auxiliary optics in a process known as frequency chirping. In an all-reflective microscope, there is no GDD since all frequencies travel at the same velocity through the system. These three benefits highlight the flexibility of all-reflective microscopy to perform imaging in numerous modalities with varying wavelength ranges without altering the system, and particularlyits utility in spectrally demanding applications such as three-photon excitation microscopy.

[0021] The potential of reflective systems to overcome these limitations has been recognized, but many proposed configurations include limitations that make those systems inefficient, cost prohibitive or ineffective for many applications. For example, some all-reflective systems include obscurations that limit throughput, contribute diffraction artifacts, and increase the risk of stray light. The unobscured systems that have been proposed often include refractive elements in the objective or tube lens, and the truly all-reflective systems include obscurations in the objective, can be difficult to produce, and / or cannot be implemented with a compact footprint. Therefore, an unobscured, compact, and efficient reflective microscope objective with high numerical aperture (NA) is the missing element that has prevented the implementation of true all- reflective microscopy. The disclosed technology of this patent document can be implemented in various embodiments to produce such an objective. The disclosed embodiments include freeform optical surface descriptions that enable objective configurations with a high NA which are more efficient than standard approaches (e.g., XY polynomials), enabling new designs as shown in the below examples.Wave Aberration Polynomial Freeform Surface

[0022] The bilateral symmetric wave aberration function is given by:

[0023] In the above equation, H is the normalized field vector, p is the normalized pupil vector, i is a unit vector that indicates the plane of symmetry, and k, m, n, p, and q are integers that define aberration coefficients W2k+n+p 2m+n+q n p q. A fundamental result of plane symmetric aberration theory is that wavefront deformations (in the exit pupil) remain the same as in rotationally symmetric systems, but additional terms appear with varying field dependence. A useful freeform surface can be defined to affect these additional terms by considering dot products independent of H:

[0024] Converting to Cartesian coordinates yields the following description of freeform departure for a so-called "wave aberration polynomial" freeform surface:

[0025] where d = (a - b) and Adbare weighting coefficients. The coefficients d and b for an arbitrary polynomial term j are given byG (f)[G (f) + 3] . d(j) = - - J

[0026] In the above equations, G(J) is the term's grouping order, given by:

[0027] This polynomial surface type is essentially a subset of XY polynomial terms, but its fundamental connection to the aberrations of plane symmetric systems provides access to high order surface correction without inundating the optimization algorithm with redundant variables. The following example designs have been realized with this surface type, although they could have theoretically been achieved using any of the common surface types (e.g., XY polynomials, Zernike polynomials).

[0028] Various operations disclosed herein can be implemented using a processor / controller is configured to include, or be coupled to, a memory that stores processor executable code that causes the processor / controller carry out various computations and processing of information. The processor / controller can further generate and transmit / receive suitable information to / from the various system components, as well as suitable input / output (IO) capabilities (e.g., wired or wireless) to transmit and receive commands and / or data. The processor / controller may, for example, provide signals to apply voltages and currents to the electrodes and coils that are described herein, or to selectively activate or deactivate various components or operations.Examples of Unobscured All-Reflective Microscope Objective Designs

[0029] FIG. 1 shows a four-mirror unobscured objective in accordance with an example embodiment that covers a field of view (FOV) of 1 .5 mm (diameter) at a NA of 0.50. The effective focal length of the objective is 5.0 mm and the angular semi-field of view is 8.5 degrees. The system collects light from an object in a first focal plane, forms an intermediate image, and projects a final image to an infinite distance (i.e., collimated output). In order from the object plane, the system includes a first mirror 102 that is concave, a second mirror 104 that is convex, a third mirror 106 that is concave, a fourth mirror 108 that is concave, and a physical aperture stop 110. The mirror radii may be chosen to nullify the Petzval sum. All four mirrors in the depicted configuration are freeform, and can be described by wave aberration polynomials, Zernike polynomials, XY polynomials, or any other freeform surface equation with planar symmetry.

[0030] The entrance pupil is located at infinity such that the system is object-space telecentric. An intermediate pupil plane is formed at (or near) the second mirror 104, which is then reimaged by the third 106 and fourth 108 mirrors to the physical aperture stop 110. The physical aperture stop 110 is accessible, which is convenient for manufacturing as well as for concatenating the objective with other optical subassemblies.

[0031] The objective can be understood as two groups. The first 102 and second 104 mirrors form the first group, which collects light emitted from an object and forms an intermediate image between the second 104 and third 106 mirrors. The chief ray is propagating away from the optical axis through the object after reflection from the second mirror 104. The third 106 and fourth 108 mirrors form the second group, which acts as a field mirror group to redirect the chief ray back toward the object's optical axis. This arrangement of groups is beneficial to keeping the system compact. It is notable that in this configuration, the chief ray between the fourth mirror 108 and physical aperture stop 110 crosses over the chief ray between the second 104 and third 106 mirrors. This allows for a compact arrangement of the third 106 and fourth 108 mirrors.

[0032] The working distance for the example configuration of FIG. 1 is 16.0 mm and is limited by the angle of incidence on the first 102 and second 104 mirrors.

[0033] FIG. 2 shows a four-mirror objective configuration in accordance with another example embodiment that covers a FOV of 700 pm (diameter) at a NA of 0.70.This configuration provides diffraction limited imaging across the FOV for all wavelengths above 215 nm. Today's state-of-the-art applications of UV microscopy extend down to approximately 240nm, so this embodiment can provide exceptional image quality for all useful wavelength bands from UV to IR. For this example configuration, the effective focal length of the objective is 10.0 mm and the angular semi-field of view is 2.0 degrees. The system collects light from an object in a first focal plane, forms an intermediate image, and projects a final image to an infinite distance (i.e., collimated output). In orderfrom the object plane, the system includes a first mirror 202 that is concave, a second mirror 204 that is convex, a third mirror 206 that is concave, a fourth mirror 208 that is concave, and a physical aperture stop 210. The mirror radii may be chosen to nullify the Petzval sum. In the example configuration of FIG. 2, all four mirrors are freeform, and can be described by wave aberration polynomials, Zernike polynomials, XY polynomials, or any other freeform surface equation with planar symmetry.

[0034] The entrance pupil is located at infinity such that the system is object-space telecentric. An intermediate pupil plane is formed at (or near) the second mirror 204, which is then reimaged by the third 206 and fourth 208 mirrors to the physical aperture stop 210. The physical aperture stop 210 is accessible, which is convenient for manufacturing as well as for concatenating the objective with other optical subassemblies.

[0035] The objective can be understood as two groups. The first 202 and second 204 mirrors form the first group, which collects light emitted from an object and forms an intermediate image between the second 204 and third 206 mirrors. The chief ray is propagating away from the optical axis through the object after reflection from the second mirror 204. The third 206 and fourth 208 mirrors form the second group, which acts as a field mirror group to redirect the chief ray back toward the object's optical axis. It is notable that in this configuration, the chief ray between the fourth mirror 208 and physical aperture stop 210 does not cross over the chief ray between the second 204 and third 206 mirrors as in the example configuration of FIG. 1. The tilt of the fourth mirror 208 has the opposite sign from its value in the example configuration of FIG. 1 , representing a different aberration balancing strategy.

[0036] The working distance of the example objective of FIG. 2 is 5.0 mm and is limited by the angle of incidence on the first 202 and second 204 mirrors.

[0037] These two example configurations of FIGS. 1 and 2 provide the benefit of high NA over a relatively large FOV. These are the geometrical layouts required to support such specifications. However, it may be of practical use to have an unobscured reflective objective that is compatible with commercially available microscopes. FIG. 3 shows a third configuration of an objective in accordance with another example embodiment that features an object plane and physical aperture stop whose optical axes are coaxial with one another. In this way, the objective, when inserted into the commercial system, remains coaxially aligned with existing illumination and image relay optics. In the example configuration of FIG. 3, the axial distance from the physical aperture stop to the object plane is 45.0 mm, which matches the parfocal distance of typical commercial objectives such that the objective can be readily incorporated in a standard microscope objective turret. The outer diameter of the example configuration of FIG. 3 is 46.0 mm. This configuration covers a FOV of 1.24 mm (diameter) at a NA of 0.25. The effective focal length of the objective is 17.8 mm and the angular semifield of view is 2.0 degrees. The working distance of this configuration is 6.7 mm.

[0038] The system collects light from an object in a first focal plane, forms an intermediate image, and projects a final image to an infinite distance (i.e., collimated output). Uniform coma is prominent in the intermediate image plane. In order from the object plane, the system includes a first mirror 302 that is concave, a second mirror 304 that is concave, a third mirror 306 that is concave, a fourth mirror 308 that is convex, and a physical aperture stop 310. The mirror radii may be chosen to nullify the Petzval sum. In the example configuration of FIG. 3, all four mirrors are freeform, and can be described by wave aberration polynomials, Zernike polynomials, XY polynomials, or any other freeform surface equation with planar symmetry.

[0039] The entrance pupil is located at infinity such that the system is object-space telecentric. An intermediate pupil plane is formed between the second 304 and third 306 mirrors, which is then reimaged by the third 306 and fourth 308 mirrors to the physical aperture stop 310. The physical aperture stop 310 is accessible, which is convenient for manufacturing as well as for concatenating the objective with other optical subassemblies.

[0040] The example objective of FIG. 3 may be understood as two groups designed to balance low order plane symmetric aberrations between one another. The first 302 and second 304 mirrors form the first group, and the third 306 and fourth 308 mirrors form the second group. The fourth mirror 308 contributes significant uniform coma due to its large tilt angle and marginal ray height. To counteract this, the first mirror group produces an intermediate image with significant uniform coma of the opposite sign from that of the second mirror group.

[0041] One of key concepts associated with the example embodiments of the unobscured all-reflective objectives is that of the local optical axis of each mirror in the system. The traditional methods to design unobscured reflective systems use off-axis segments of rotationally symmetric surfaces with an off-axis object and image. In this way, the local optical axis of each mirror is colinear with a global optical axis for the entire system. For example, in FIG. 4 (reproduced from U.S. Patent No. 5,815,310), each mirror is rotationally symmetric about OA. The shaded shapes represent the physical extent of the mirrors to be fabricated, but the dotted line of each surface (e.g., 12') indicates the extended surface profile that is rotationally symmetric about OA. The object and image (reticle and wafer) are off axis to provide an unobscured optical path through these mirror segments.

[0042] In example embodiments of the unobscured all-reflective objective described herein, the local optical axes of the mirrors are not colinear with any global optical axis. Instead, as shown in FIG. 5 (similar to the configuration of FIG. 2) mirrors are allowed to be tilted in a common plane and joined by a so-called optical axis ray that passes through the center of each mirror's base radius. In this context, the "base radius" is the radius of the spherical surface that the aspheric or freeform departure is applied to. Said another way, it is common to discuss the "aspheric departure" or "freeform departure" - the base radius is the radius of the spherical shape from which the surface is departing. Additional explanations are provided below under the heading "Departure from Base Surface."

[0043] Referring back to FIG. 5, it is noted that a unique local optical axis exists at each mirror (dash-dot line) around which the base radius is rotationally symmetric. This also holds true for other embodiments disclosed herein. Plane symmetric freeformoverlays have their origins at these local axes. For example, the origin can be defined as x,y) = (0,0) on the freeform surface whose sag is described by:

[0044] where C is the surface curvature and Aj are weighting coefficients for the terms of a general freeform surface W(x, y). This means that the base spherical surface is centered upon the surface's local axis, as is the freeform overlay.

[0045] In the example configuration of FIG. 5, the local optical axes of M1 and M2 appear decentered because the apertures have been cropped asymmetrically due to packaging considerations. As such, the disclosed embodiments provide more flexibility in designing and manufacturing of all-reflective objectives to allow higher NAs, improved image quality, more compact footprints, and the added flexibility to vary the geometrical configuration of the reflective components as necessitated by different applications.

[0046] Referring back to FIG. 4, the aperture stop is located at M2', which is located internally within the objective, and whose local optical axis is colinear with the global optical axis OA. This is in contrast to the objective lens configurations disclosed herein. As illustrated in, for example, FIG. 5, the aperture stop, AS, is normal to and concentric with the optical axis ray. This also holds true for other embodiments disclosed herein. The freeform overlays on each mirror have their mathematical origin at the local optical axis. This construction allows for planar symmetric freeform mirrors, rather than rotationally symmetric ones, which provides the opportunity for superior aberration correction.Example MTF Comparison Between Global Optical Axis and Non-Colinear Local Optical Axes

[0047] To illustrate the superior aberration correction of systems designed in accordance with the disclose embodiments having mirrors with local optical axes that are not colinear, a comparison is made between such a design and a rotationally symmetric design where all mirrors share a global optical axis (taken from the literature). The MTF (modulation transfer function) provides a quantitative characterization of a system's image quality and is commonly used to compare imaging systems in the field of optical engineering. A design is considered better when the MTF is higher; the upperlimit is determined by diffraction theory and is approximately a triangle function centered about the origin.

[0048] FIG. 6 shows example MTF plots for the two designs. The top plot corresponds to a rotationally symmetric design using prior techniques, and the bottom plot corresponds to a freeform design with tilted mirrors in accordance with an example embodiment. As shown in the plots, the design with tilted freeform mirrors achieves a more ideal MTF, indicating superior performance. Also of note is the cutoff frequency for the tilted freeform design is approximately 3700 cycles / mm, whereas the rotationally symmetric design cuts off at 3200 cycles / mm. This indicates that the tilted freeform design not only has better aberration correction but can also achieve higher resolution.

[0049] The design taken from the literature (top) also has significant anamorphic distortion (-40%), which is undesirable. This is not present in the tilted freeform design, which further demonstrates the correction ability of this design approach.Efficiency of Wave Aberration Polynomial vs. Standard Freeform Descriptions

[0050] As noted earlier, the mirrors in the depicted configurations of the all- reflective objective are freeform, and can be described by wave aberration polynomials, Zernike polynomials, XY polynomials, or any other freeform surface equation with planar symmetry. However, in accordance with some embodiments, those surfaces can be more efficiently designed using wave aberration polynomial representations described earlier. To illustrate the gains, the efficiency of the wave aberration polynomial freeform description was tested by comparing against an existing freeform design (four-mirror microscope objective with NA = 0.50) that utilized a hybrid mixture of Zernike polynomials and XY polynomials. The freeform surface description of the existing design was converted to a wave aberration polynomial representation using as many terms as required. To compare the efficiency of the two surface representations, the total number of freeform terms used on the four mirrors is used as a figure of merit (fewer is better).

[0051] The Zernike / XY polynomial design required 148 freeform terms to describe the four surfaces. The wave aberration polynomial design required 100 terms to achieve similar performance, representing a 32% decrease in variables. The wave aberration polynomial design was then further optimized to remove redundant freeformterms and minimize the total number of variables. This refined design required only 63 terms to achieve similar performance, representing a 57% decrease in variables.

[0052] The fundamental connection between the wave aberration polynomial freeform surface type and the bilateral symmetric wave aberration function provides an efficiency advantage to the designer. With this surface, it is possible that designers can achieve high quality designs with less optimization time and lower computational resources.Example Procedure for Optimizing a Design

[0053] To begin optimization, the wavelength is set to 13 nm and a merit function targeting minimum RMS wavefront error is generated. Although the system will be employed in optical microscopy (-240 nm - 3 pm), minimizing wavefront error in the EUV leads to starting geometries with exceptional promise for aberration correction.

[0054] Next, the target numerical aperture (NA) and field of view are chosen based on application needs. It is common practice in optical design to begin a design at low NA and gradually increase the aperture until the desired final NA is achieved. An often- limiting challenge in unobscured reflective systems with high NA is ensuring the first and second mirrors are tilted sufficiently to avoid obscuration (e.g., M1 and M2 in FIG. 5). In our approach, we opt to begin the design process in such a way that these two mirrors provide the necessary clearance from the outset by defining a conical region that covers the desired final NA and which is declared to be off-limits for all but the first mirror.

[0055] In the initial configuration, the system is laid out with the full field of view at a low relative aperture (e.g., NA = 0.05). Mirrors are tilted to clear the conical off-limits region and freeform overlays are added to correct the system for uniform astigmatism, uniform coma, linear astigmatism, field tilt, anamorphic distortion, keystone distortion, and smile distortion. The wave aberration polynomial freeform surface is a convenient choice for this, since only two freeform terms are required (j=4 and j=5) at each surface; these terms are comatic and astigmatic in shape, respectively. Additionally, fourthorder rotationally symmetric aberrations are corrected by use of a fourth-order aspheric departure 0=3 term of the wave aberration polynomial (WAP)) on each mirror, for a totalof three freeform terms per mirror. Field curvature is corrected by suitable choice of base radii for the mirrors to nullify the Petzval sum.

[0056] Note that WAP terms 3-5 constitute the entirety of WAP terms with grouping order 2 (GO) = 2); we may call these the "group two terms". At this time, other geometric requirements may be enforced, such as working distance and remote stop. FIG. 7 shows the geometry of such a starting configuration. In this example, the starting low NA (0.05) for target NA of 0.70 with four mirrors and an external aperture stop are selected. A geometric constraint is enforced to keep M2-M4 out of the off-limits cone required for M1 to achieve the desired final NA. Requirements for a finite working distance (WD) and an accessible / remote stop are also added at this point.

[0057] Due to the low NA of the starting configuration, correcting for the aberrations mentioned above should provide diffraction limited imaging performance in the EUV since higher order aberrations are negligible at this relative aperture. From here, the aperture stop diameter is gradually increased and the design is re-optimized at NA increments of 0.025. When the RMS wavefront error grows larger than approximately 1 .0 waves (at A=13 nm), the next group of WAP freeform terms is added and optimization continues until the desired NA is reached. FIG. 8 shows some sample configurations with increasing NA that follow this process.

[0058] Note that in FIG. 8, each design maintains the geometric constraints laid out in FIG. 7, but the individual mirror spacings and tilts maintain the freedom to navigate the solution space and arrive at an optimal final design. In other words, mirror spacings and tilts are allowed to vary without stalling the optimization algorithm. This is a key advantage of using the wave aberration polynomial freeform surface description, owing to its fundamental connection to the bilateral symmetric wave aberration function as discussed previously. The final design shown in FIG. 8 (NA = 0.700) has an RMS wavefront error of 1.154 waves at A=13 nm, which corresponds to an RMS wavefront error of 0.0698 waves at A=215 nm. It is common to declare a system with RMS wavefront error less than 0.07 waves as diffraction limited, which is why the system was quoted earlier as having diffraction limited performance down to a wavelength of 215 nm.

[0059] The following provides a set of procedures for designing an objective in accordance with some example embodiments.Select desired NA and FOV based on application. Use NA to define off-limits conical region that mirrors may not enter. Input desired number of mirrors and tilt such that every mirror after the first is outside of the off-limits conical region. Set the aperture stop diameter such that the NA at the sample is low (e.g., NA = 0.05), Set the field definition to cover the desired full field of view of the final system. Set the wavelength to EUV (e.g., 13 nm). Generate merit function that minimizes RMS wavefront error. Add low-order freeform terms (e.g., WAP terms with grouping order of 2) to control rotationally symmetric and plane symmetric fourth-order aberrations, a. Field curvature corrected by base radii of mirrors. b. Spherical aberration, linear coma, quadratic astigmatism, cubic distortion corrected by j=3 WAP terms. c. Uniform astigmatism, uniform coma, linear astigmatism, field tilt, anamorphic distortion, smile distortion, keystone distortion corrected by j=4 and j=5 WAP terms and mirror tilts. Add additional geometric constraints to merit function to control relevant requirements, such as working distance, remote stop, and unobstructed optical path. Optimize until the system is diffraction limited. Variables include mirror radii, air gap thicknesses, mirror tilts, and freeform terms. Increase the NA by one step (e.g., by 0.025); this can be done, for example, by increasing the aperture stop diameter. Optimize with same variables as step 9. Repeat steps 11 -12 until the minimum achievable RMS wavefront error is greater than ~1 .0 waves (at A=13 nm). Then, add the next group of WAP freeform terms and continue optimization. Repeat steps 11-13 until the final design is achieved.Departure from Base Surface

[0060] The following discussion is provided to facilitate the understanding of some of the disclosed concepts related to departure of the aspherical surfaces from a spherical shape. Mathematically, the sag of a rotationally symmetric conic surface is given by:Cs2Z(s) = -1 + Vl - (l + / r)C2s2

[0061] In the above equation, C is the curvature of the surface, k is the conic constant of the surface, and s is the radial distance from the optical axis. If we set Ato zero, the result is a spherical surface. To represent a rotationally symmetric even aspheric surface, the equation becomes:

[0062] The first term in the above equations is the base spherical / conic surface (which is described using its "base radius") and aspheric terms are added on top of it. The following representation can be used to describe a wave aberration polynomial freeform surface:

[0063] In this equation, x,y locate a point on the freeform surface, Aj is the weighting coefficient for W), the jthterm of the wave aberration polynomial, and N total polynomial terms are added on top of the base spherical surface. Note that, in example implementation, we have set k equal to zero so that the base surface is spherical, not conic. This is to avoid redundancy with the j=3 term, which is a 4thorder rotationally symmetric deformation and can be approximated as equivalent to the conic deformation.

[0064] FIG. 9 illustrates a set of operations that can be performed for producing an all-reflective objective lens configuration in accordance with an example embodiment. At 902, a target numerical aperture (NA), a target field of view (FOV), and a number of mirrors for the all-reflective objective lens configuration are obtained orselected, where the number of mirrors is four or more. At 904, initial tilt and location values of the mirrors are set based on a geometric constraint on at least some of the mirrors. At 906, a merit function is obtained that is configured to minimize a root mean square (RMS) wavefront error associated with the objective lens configuration, the merit function being based on low-order freeform terms and geometrical parameters of the objective lens configuration. At 908, using the merit function, a candidate all-reflective objective lens configuration is produced that corresponds to a diffraction limited system. At 910, in a step-wise fashion, the target NA is increased by a predetermined step value and one or more candidate all-reflective objective lens configurations is produced using the merit function until a minimum RMS wavefront error of greater than a predetermined number of waves is obtained. For example, if the target final performance is not reached, additional freeform terms are introduced and operations 908-910 are repeated.

[0065] In one example embodiment, the operations include setting a wavelength associated with the all-reflective objective lens configuration in an extreme ultraviolet (EUV) range. In another example embodiment, the geometrical region includes an off- limits cone that excludes all but one of the mirrors. In yet another example embodiment, the low-order freeform terms include wave aberration polynomial terms for characterizing freeform surfaces of the mirrors, and are configured to control rotationally symmetric and plane symmetric aberrations. In still another example embodiment, the predetermined step value is 0.025.

[0066] According to another example embodiment, the predetermined number of waves is one wave. In one example embodiment, in each step that includes increasing the NA, one or more additional freeform terms are added. In another example embodiment, the aberrations associated with surfaces of the mirrors are represented using a wave aberration polynomial freeform format.

[0067] Another aspect of the disclosed embodiments relates to an all-reflective objective lens configuration that includes at least four mirrors, wherein each of the at least four mirrors includes a freeform surface, and each of the at least four mirrors is positioned within the all-reflective objective lens configuration to allow light from an object to enter the all-reflective objective lens configuration and reflect from each of the at least four mirrors only once before reaching a location of an aperture stop identifyingan exit location of the all-reflective objective lens configuration. In the all-reflective objective lens configuration, the at least four mirrors are positioned within the all- reflective objective lens configuration to provide an unobscured field of view, a local optical axis of each of the at least four mirrors is not colinear with a global optical axis of the all-reflective objective lens configuration, and the aperture stop is not positioned internal to the all-reflective objective lens configuration.

[0068] In one example embodiment, the local optical axis of each of the at least four mirrors is identified with respect to an optical axis ray. In another example embodiment, the freeform surface of each of the at least four mirrors is a freeform overlay on a reflective surface, and the optical axis ray passes through a center of each reflective surface's base radius. In still another example embodiment, the aperture stop is physically accessible to allow concatenation of the all-reflective objective lens configuration to another optical system. In yet another example embodiment, the at least four mirrors consist of a first mirror that is concave, a second mirror that is convex, a third mirror that is concave, a fourth mirror that is concave, an entrance pupil of the all-reflective objective lens configuration is located at infinity, and an intermediate pupil plane is located at or near the second mirror that is reimaged by the third mirror and the fourth mirror to the aperture stop.

[0069] According to another example embodiment, a tilt and a position of at least the fourth mirror is selected to allow a chief ray between the fourth mirror and the aperture stop to cross over a chief ray between the second mirror and third mirror. In one example embodiment, the all-reflective objective lens configuration has a field of view (FOV) of 1.5 mm and a numerical aperture (NA) of 0.50. In another example embodiment, a tilt and a position of at least the fourth mirror is selected to prevent any rays between the fourth mirror and the aperture stop to cross over any rays between the second mirror and third mirror. In still another example embodiment, the all- reflective objective lens configuration has a field of view (FOV) of 700 microns and a numerical aperture (NA) of 0.70.

[0070] In another example embodiment, the at least four mirrors consist of a first mirror that is concave, a second mirror that is concave, a third mirror that is concave, a fourth mirror that is convex, an entrance pupil of the all-reflective objective lens configuration is located at infinity, optical axes of an object plane and the aperture stopare coaxial with one another, and an intermediate pupil plane is located at or near the second mirror that is reimaged by the third mirror and the fourth mirror to the aperture stop. In one example embodiment, the first and the second mirrors form a first mirror group configured to produce an intermediate image with a particular amount of uniform coma having an opposite sign to a coma generated by a second mirror group that consists of the third and the fourth mirrors. In yet another example embodiment, the all-reflective objective lens configuration has a field of view (FOV) of 1.24 mm and a numerical aperture (NA) of 0.25.

[0071] Various operations disclosed herein can be implemented using a processor / controller is configured to include, or be coupled to, a memory that stores processor executable code that causes the processor / controller carry out various computations and processing of information. The processor / controller can further generate and transmit / receive suitable information to / from the various system components, as well as suitable input / output (IO) capabilities (e.g., wired or wireless) to transmit and receive commands and / or data. The processor / controller may, for example, provide signals to control the operation of various components such as lasers and detectors that are disclosed herein. The processor / controller may be further configured to perform various method steps and computations that are disclosed in this patent document.

[0072] Various information and data processing operations described herein may be implemented in one embodiment by a computer program product, embodied in a computer-readable medium, including computer-executable instructions, such as program code, executed by computers in networked environments. A computer- readable medium may include removable and non-removable storage devices including, but not limited to, Read Only Memory (ROM), Random Access Memory (RAM), compact discs (CDs), digital versatile discs (DVD), etc. Therefore, the computer-readable media that is described in the present application comprises non- transitory storage media. Generally, program modules may include routines, programs, objects, components, data structures, etc. that perform particular tasks or implement particular abstract data types. Computer-executable instructions, associated data structures, and program modules represent examples of program code for executing steps of the methods disclosed herein. The particular sequence of such executableinstructions or associated data structures represents examples of corresponding acts for implementing the functions described in such steps or processes.

[0073] Only a few implementations and examples are described and other implementations, enhancements and variations can be made based on what is described and illustrated in this patent document.

Claims

CLAIMSWe claim:1 . An all-reflective objective lens configuration, comprising: at least four mirrors, wherein: each of the at least four mirrors includes a freeform surface, each of the at least four mirrors is positioned within the all-reflective objective lens configuration to allow light from an object to enter the all-reflective objective lens configuration and reflect from each of the at least four mirrors only once before reaching a location of an aperture stop identifying an exit location of the all-reflective objective lens configuration, the at least four mirrors are positioned within the all-reflective objective lens configuration to provide an unobscured field of view, a local optical axis of each of the at least four mirrors is not colinear with a global optical axis of the all-reflective objective lens configuration, and the aperture stop is not positioned internal to the all-reflective objective lens configuration.

2. The all-reflective objective lens configuration of claim 1 , wherein the local optical axis of each of the at least four mirrors is identified with respect to an optical axis ray.

3. The all-reflective objective lens configuration of claim 2, wherein the freeform surface of each of the at least four mirrors is a freeform overlay on a reflective surface, and the optical axis ray passes through a center of each reflective surface's base radius.

4. The all-reflective objective lens configuration of claim 1 , wherein the aperture stop is physically accessible to allow concatenation of the all-reflective objective lens configuration to another optical system.

5. The all-reflective objective lens configuration of claim 1 , wherein: the at least four mirrors consist of a first mirror that is concave, a second mirror that is convex, a third mirror that is concave, a fourth mirror that is concave, an entrance pupil of the all-reflective objective lens configuration is located at infinity, and an intermediate pupil plane is located at or near the second mirror that is reimaged by the third mirror and the fourth mirror to the aperture stop.

6. The all-reflective objective lens configuration of claim 5, wherein a tilt and a position of at least the fourth mirror is selected to allow a chief ray between the fourth mirror and the aperture stop to cross over a chief ray between the second mirror and third mirror.

7. The all-reflective objective lens configuration of claim 6, wherein the objective lens configuration has a field of view (FOV) of 1.5 mm and a numerical aperture (NA) of 0.50.

8. The all-reflective objective lens configuration of claim 5, wherein a tilt and a position of at least the fourth mirror is selected to prevent any rays between the fourth mirror and the aperture stop to cross over any rays between the second mirror and third mirror.

9. The all-reflective objective lens configuration of claim 8, wherein the all- reflective objective lens configuration has a field of view (FOV) of 700 microns and a numerical aperture (NA) of 0.70.

10. The all-reflective objective lens configuration of claim 1 , wherein: the at least four mirrors consist of a first mirror that is concave, a second mirror that is concave, a third mirror that is concave, a fourth mirror that is convex, an entrance pupil of the all-reflective objective lens configuration is located at infinity,optical axes of an object plane and the aperture stop are coaxial with one another, and an intermediate pupil plane is located at or near the second mirror that is reimaged by the third mirror and the fourth mirror to the aperture stop.11 . The all-reflective objective lens configuration of claim 10, wherein the first and the second mirrors form a first mirror group configured to produce an intermediate image with a particular amount of uniform coma having an opposite sign to a coma generated by a second mirror group that consists of the third and the fourth mirrors.

12. The all-reflective objective lens configuration of claim 11 , wherein the all- reflective objective lens configuration has a field of view (FOV) of 1.24 mm and a numerical aperture (NA) of 0.25.

13. A method for producing an all-reflective objective lens configuration, comprising: selecting or obtaining a target numerical aperture (NA), a target field of view (FOV), and a number of mirrors for the all-reflective objective lens configuration, wherein the number of mirrors is four or more; setting initial tilt and location values of the mirrors based on a geometric constraint on at least some of the mirrors; obtaining a merit function configured to minimize a root mean square (RMS) wavefront error associated with the objective lens configuration, the merit function being based on low-order freeform terms and geometrical parameters of the objective lens configuration; using the merit function, producing a candidate all-reflective objective lens configuration that corresponds to a diffraction limited system; in a step-wise fashion, increasing the target NA by a predetermined step value and producing one or more candidate all-reflective objective lens configurations using the merit function until a minimum RMS wavefront error of greater than a predetermined number of waves is obtained.

14. The method of claim 13, comprising setting a wavelength associated with the all-reflective objective lens configuration in an extreme ultraviolet (EUV) range.

15. The method of claim 13, wherein the geometrical region includes an off- limits cone that excludes all but one of the mirrors.

16. The method of claim 13, wherein the low-order freeform terms include wave aberration polynomial terms for characterizing freeform surfaces of the mirrors, and are configured to control rotationally symmetric and plane symmetric aberrations.

17. The method of claim 13, wherein the predetermined step value is 0.025.

18. The method of claim 13, wherein the predetermined number of waves is one wave.

19. The method of claim 16, wherein in each step that includes increasing the NA, one or more additional freeform terms are added.

20. The method of claim 16, wherein aberrations associated with surfaces of the mirrors are represented using a wave aberration polynomial freeform format.

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