Measurement method and device for determining complex-valued fields

Abstract

A method for determining a complex-valued field associated with a sample measured using an imaging system is disclosed. The method includes obtaining image data associated with a series of images of the sample imaged at an image plane of the imaging system, and applying at least two different modulation functions in a Fourier plane of the imaging system to the image data; and determining a complex-valued field from the imaging data based on the applied modulation functions.

Description

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS

[0002] This application claims priority to EP application 19180565.4 filed on June 17, 2019, EP application 19195599.6 filed on September 05, 2019, and EP application 19202049.3 filed on October 08, 2019, the entire contents of which are incorporated herein by reference. Technical Field

[0003] The invention relates to a metrology device or an inspection device for determining properties of a structure on a substrate. The invention also relates to a method for determining properties of a structure on a substrate. Background Art

[0004] A lithographic apparatus is a machine configured to apply a desired pattern to a substrate. A lithographic apparatus can be used, for example, in the manufacture of integrated circuits (ICs). For example, a lithographic apparatus can project a pattern (also often referred to as a "design layout" or "design") at a pattern forming device (e.g., a mask) onto a layer of radiation-sensitive material (resist) disposed on a substrate (e.g., a wafer).

[0005] To project a pattern on a substrate, a lithographic apparatus may use electromagnetic radiation. The wavelength of this radiation determines the minimum size of features that can be formed on the substrate. Typical wavelengths currently used are 365nm (i-line), 248nm, 193nm and 13.5nm. A lithographic apparatus using extreme ultraviolet (EUV) radiation with a wavelength in the range of 4-20nm, such as 6.7nm or 13.5nm, can be used to form smaller features on a substrate compared to a lithographic apparatus using radiation with a wavelength of, for example, 193nm.

[0006] Low k1 lithography can be used to process features with dimensions smaller than the classical resolution limit of the lithographic apparatus. In such a process, the resolution formula can be expressed as CD=k1×λ / NA, where λ is the wavelength of radiation employed, NA is the numerical aperture of the projection optics in the lithographic apparatus, CD is the "critical dimension" (usually the smallest feature size printed, but in this case the half pitch), and k1 is an empirical resolution factor. In general, the smaller the k1, the more difficult it is to reproduce a pattern on a substrate that is similar in shape and size to that designed by the circuit designer in order to achieve a particular electrical function and performance. To overcome these difficulties, complex fine-tuning steps can be applied to the lithographic projection apparatus and / or the design layout. These include, for example, but are not limited to: optimization of NA, customized illumination schemes, use of phase-shifted patterning devices, various optimizations of the design layout (such as optical proximity correction (OPC, sometimes also referred to as "optical and process correction") in the design layout, or other methods generally defined as "resolution enhancement techniques" (RET). Alternatively, a tight control loop for controlling the stability of the lithographic apparatus can be used to improve the reproduction of patterns at low k1.

[0007] In photolithography processes, it is frequently desirable to measure the resulting structures, for example for process control and verification. Various tools for making such measurements are known, including scanning electron microscopes or various forms of metrology devices, such as scatterometers. A general term referring to such tools may be metrology device or inspection device.

[0008] A metrology device can use a computationally retrieved phase to apply an aberration correction to an image captured by the metrology device. A method for computing the phase described uses multiple different images, such as multiple images of the same target under different focusing conditions. This typically requires mechanical movement of the sample (e.g., target). Furthermore, it is assumed that movement of the sample through the focus is equivalent to detection of movement through the focus by the detector. The validity of this assumption is questionable. Furthermore, the defocus range over which this assumption is valid may be too short to obtain sufficient information for a successful reconstruction. The reconstruction itself is performed using an iterative algorithm that is computationally expensive and cannot be certain to converge to an optimal solution. Moreover, it is unclear how spatial partial coherence affects the reconstruction results. Summary of the invention

[0009] When performing complex-valued field measurements, it is desirable to reduce computation time and increase throughput.

[0010] Embodiments of the invention are disclosed in the claims and the detailed description.

[0011] In a first aspect of the present invention, a method for determining a complex-valued field associated with a sample measured using an imaging system is provided, comprising: obtaining image data associated with a series of images of the sample imaged at an image plane of the imaging system, and applying at least two different modulation functions in a Fourier plane of the imaging system to the image data; and determining the complex-valued field from the imaging data based on the applied modulation functions.

[0012] In a second aspect of the present invention, a measurement device for performing the method of the first aspect is provided, comprising: an imaging system for imaging a field reflected from a sample; at least one modulator at a Fourier plane of the imaging system for defining each modulation function; and a detector at an image plane of the imaging system for capturing each of the images. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Embodiments of the invention will now be described, by way of example only, with reference to the accompanying schematic drawings, in which:

[0014] - Figure 1 A schematic diagram of a photolithography apparatus is depicted;

[0015] - Figure 2 A schematic diagram of a lithography unit is depicted;

[0016] - Figure 3 Depicted is a schematic representation of overall lithography showing the collaboration between three key technologies to optimize semiconductor manufacturing;

[0017] - Figure 4 is a schematic diagram of the scatterometry setup;

[0018] - Figure 5 is a schematic diagram of a measuring device according to an embodiment of the present invention;

[0019] - Figure 6 is a schematic diagram of a first non-iterative method for determining a complex-valued field according to an embodiment of the present invention;

[0020] - Figure 7 It is available for Figure 6 Schematic diagram of two mask pairs of the illustrated method;

[0021] - Figure 8 is a schematic diagram of a measuring device according to another embodiment of the present invention;

[0022] - Fig. 9 is a schematic diagram of a measuring device according to another embodiment of the present invention;

[0023] - Fig.10 is a schematic diagram of a grating mask that can be used for a second non-iterative method for determining a complex-valued field according to an embodiment of the present invention;

[0024] - Fig.11 is a schematic diagram of a third non-iterative method for determining a complex-valued field according to an embodiment of the present invention;

[0025] - Fig.12 is a schematic diagram of a fourth non-iterative method for determining a complex-valued field according to an embodiment of the present invention;

[0026] - Fig.13 is a schematic diagram of a fifth non-iterative method for determining a complex-valued field according to an embodiment of the present invention;

[0027] - Fig.14 are schematic diagrams of (a), (b) and (c) as follows, wherein (a) is a measurement device according to an embodiment applicable to zero-order self-referenced holography; (b) and (c) are Fig.14 Specific details of an optional split objective lens embodiment of the measurement device of (a);

[0028] - Fig.15 is a schematic diagram of a measurement device according to an embodiment suitable for a Lee hologram-based method.

[0029] - Fig.16 is a schematic diagram of an iterative method for determining a complex-valued field according to an embodiment of the present invention; and

[0030] - Fig.17 is a block diagram illustrating a computer system that can help implement methods according to embodiments of the present invention. DETAILED DESCRIPTION

[0031] In this document, the terms "radiation" and "beam" are used to cover all types of electromagnetic radiation, including UV radiation (e.g. having a wavelength of 365, 248, 193, 157 or 126 nm) and EUV (extreme ultraviolet radiation, e.g. having a wavelength in the range of about 5-100 nm).

[0032] The terms "reticle", "mask" or "patterning device" as used herein may be broadly interpreted as referring to a general patterning device that can be used to impart an incident radiation beam with a patterned cross-section that corresponds to the pattern to be produced in a target portion of the substrate. The term "light valve" may also be used herein. In addition to classical masks (transmissive or reflective, binary, phase-shifting, hybrid, etc.), other examples of such patterning devices include programmable mirror arrays and programmable LCD arrays.

[0033] Figure 1A lithographic apparatus LA is schematically shown. The lithographic apparatus LA comprises an illumination system (also referred to as an illuminator) IL configured to condition a radiation beam B (e.g., UV radiation, DUV radiation, or EUV radiation), a mask support (e.g., a mask stage) MT configured to support a patterning device (e.g., a mask) MA and connected to a first positioner PM configured to accurately position the patterning device MA according to certain parameters, a substrate support (e.g., a wafer stage) WT configured to hold a substrate (e.g., a resist-coated wafer) W and connected to a second positioner PW and the wafer stage WT configured to accurately position the substrate support according to certain parameters, and a projection system (e.g., a refractive projection lens system) PS configured to project a pattern imparted to the radiation beam B by the patterning device MA onto a target portion C (e.g., comprising one or more dies) of the substrate W.

[0034] In operation, the illumination system IL receives a radiation beam from a radiation source SO, for example via a beam delivery system BD. The illumination system IL may include various types of optical components, such as refractive, reflective, magnetic, electromagnetic, electrostatic and / or other types of optical components, or any combination thereof, for directing, shaping and / or controlling the radiation. The illuminator IL may be used to condition the radiation beam B so that it has a desired spatial and angular intensity distribution in its cross-section at the plane of the patterning device MA.

[0035] The term "projection system" PS as used herein should be broadly interpreted as including various types of projection systems, including refractive, reflective, catadioptric, anamorphic, magnetic, electromagnetic and / or electrostatic optical systems, or any combination thereof, depending on the exposure radiation used, and / or other factors such as the use of an immersion liquid or the use of a vacuum. Any use of the term "projection lens" herein may be considered synonymous with the more general term "projection system" PS.

[0036] The lithographic apparatus LA may be of a type in which at least a portion of the substrate may be covered by a liquid having a relatively high refractive index, such as water, so as to fill the space between the projection system PS and the substrate W - this is also known as immersion lithography. More information on immersion techniques is given in US 6952253, which is incorporated herein by reference.

[0037] The lithographic apparatus LA may also be of a type having two or more substrate supports WT (also referred to as "dual stage"). In such a "multi-stage" machine, the substrate supports WT may be used in parallel, and / or a step of preparing a substrate W for subsequent exposure may be performed on a substrate W on one of the substrate supports WT while another substrate W on another substrate support WT is used to expose a pattern on another substrate W.

[0038] In addition to the substrate support WT, the lithographic apparatus LA may comprise a measuring table. The measuring table is arranged to hold sensors and / or cleaning equipment. The sensors may be arranged to measure characteristics of the projection system PS or characteristics of the radiation beam B. The measuring table may accommodate a plurality of sensors. The cleaning equipment may be arranged to clean a part of the lithographic apparatus, for example a part of the projection system PS or a part of a system for providing immersion liquid. The measuring table may be moved under the projection system PS when the substrate support WT is away from the projection system PS.

[0039] In operation, a radiation beam B is incident on a patterning device (e.g. a mask) MA held on a mask support MT and is patterned by a pattern (design layout) present on the patterning device MA. After passing through the mask MA, the radiation beam B passes through a projection system PS which focuses the radiation beam onto a target portion C of the substrate W. With the aid of a second positioner PW and a position measurement system IF, the substrate support WT can be accurately moved, for example in order to position different target portions C in a focused and aligned position in the path of the radiation beam B. Similarly, a first positioner PM and possibly another position sensor ( Figure 1 The patterning device MA may be accurately positioned relative to the path of the radiation beam B using mask alignment marks M1, M2 and substrate alignment marks P1, P2. Although the substrate alignment marks P1, P2 are shown occupying dedicated target portions, they may be located in spaces between target portions. When the substrate alignment marks P1, P2 are located between target portions C, they are referred to as scribe-lane alignment marks.

[0040] like Figure 2 As shown, the lithography apparatus LA may form part of a lithography cell LC, sometimes also referred to as a lithography cell or (lithography) cluster, which typically also includes apparatus for performing pre-exposure and post-exposure processing on a substrate W. Conventionally, these include: a spin coater SC for depositing a resist layer; a developer DE for developing the exposed resist; a cooling plate CH and a baking plate BK, for example for regulating the temperature of the substrate W, for example in order to regulate the solvent in the resist layer. A substrate handler or robot RO picks up substrates W from input / output ports I / O1, I / O2, moves substrates W between different processing apparatuses, and transfers substrates W to a loading bay LB of the lithography apparatus LA. The devices in the lithography cell, which are also generally referred to as a track, are typically under the control of a track control unit TCU, which itself may be controlled by a monitoring system SCS, which may also control the lithography apparatus LA, for example via the lithography control unit LACU.

[0041] In order for substrates W exposed by the lithography apparatus LA to be correctly and consistently exposed, it is desirable to inspect the substrates to measure characteristics of the patterned structures, such as overlay errors between subsequent layers, line thickness, critical dimensions (CD), etc. For this purpose, an inspection tool (not shown) may be included in the lithography cell LC. If errors are detected, then, for example, adjustments may be made to the exposure of subsequent substrates or to other processing steps to be performed on the substrate W, particularly if the inspection is completed before other substrates W of the same batch or stack are yet to be exposed or processed.

[0042] The inspection apparatus, which may also be referred to as a metrology apparatus, is used to determine properties of a substrate W, in particular how properties vary from one substrate to another W or how properties associated with different layers of the same substrate W vary from layer to layer. Alternatively, the inspection apparatus may be configured to identify defects on the substrate W and may, for example, be part of the lithography cell LC, or may be integrated into the lithography apparatus LA, or may even be a stand-alone device. The inspection apparatus may measure properties on a latent image (the image in the resist layer after exposure), or a semi-latent image (the image in the resist layer after a post-exposure bake step PEB), or a developed resist image (wherein exposed or unexposed parts of the resist have been removed), or even an etched image (after a pattern transfer step such as etching).

[0043] Typically, the patterning process in the lithography apparatus LA is one of the most critical steps in the process, which requires high precision in the dimensional design and arrangement of the structures on the substrate W. In order to ensure this high precision, the three systems can be combined in a Figure 3 . One of these systems is a lithography apparatus LA which is (virtually) connected to a metrology tool MET (a second system) and a computer system CL (a third system). The key to this "holistic" environment is to optimize the cooperation between these three systems to enhance the overall process window and to provide a tight control loop to ensure that the patterning performed by the lithography apparatus LA remains within the process window. The process window defines the range of process parameters (e.g. dose, focus, overlay) within which a particular manufacturing process produces a defined result (e.g. a functional semiconductor device) - typically within which variations in process parameters in the lithography process or patterning process are allowed.

[0044] The computer system CL can use the (partial) design layout to be patterned to predict which resolution enhancement techniques to use and perform computational lithography simulations and calculations to determine which mask layouts and lithography apparatus settings achieve the maximum overall process window for the patterning process (in Figure 3Typically, the resolution enhancement technique is arranged to match the patterning possibilities of the lithographic apparatus LA. The computer system CL may also be used to detect where within the process window the lithographic apparatus LA is currently operating (e.g. using input from a metrology tool MET) to predict whether resolution enhancement techniques are being employed due to, for example, suboptimal processing (e.g., Figure 3 There is a defect (depicted by the arrow pointing to "0" in the second scale SC2).

[0045] The metrology tool MET may provide input to the computer system CL to enable accurate simulations and predictions, and may provide feedback to the lithographic apparatus LA to identify, for example, possible drifts in the calibration state of the lithographic apparatus LA (e.g., Figure 3 SC3 is depicted by multiple arrows in the third scale SC3).

[0046] In photolithographic processes, it is frequently desirable to make measurements of the structures produced, for example for process control and verification. Various tools for making such measurements are known, including scanning electron microscopes or various forms of metrology devices, such as scatterometers. Examples of known scatterometers typically rely on providing dedicated metrology targets, such as underfilled targets (targets in the form of simple gratings or overlaid gratings in different layers, which are large enough that the measurement beam produces a spot smaller than the grating) or overfilled targets (whereby the illumination spot partially or completely encompasses the target). Furthermore, the use of metrology tools, such as angle-resolved scatterometers that illuminate underfilled targets such as gratings, allows the use of so-called reconstruction methods, where the properties of the grating can be calculated by simulating the interaction of the scattered radiation with a mathematical model of the target structure and comparing the simulation results with the measurement results. The parameters of the model are adjusted until the simulated interaction produces a diffraction pattern similar to that observed from a real target.

[0047] Scatterometers are versatile instruments that allow measuring parameters of a lithographic process by having a sensor in the pupil or in a plane conjugate to the pupil of the scatterometer's objective (measurements are usually referred to as pupil-based measurements), or by having a sensor in the image plane or in a plane conjugate to the image plane (in this case, measurements are usually referred to as image-based or field-based measurements). Such scatterometers and related measurement techniques are further described in patent applications US20100328655, US2011102753A1, US20120044470A, US20110249244, US20110026032 or EP1,628,164A, which are hereby incorporated by reference in their entirety. The aforementioned scatterometers can measure multiple targets from multiple gratings in one image using light from soft x-rays as well as visible-near IR wave ranges.

[0048] Figure 4A metrology device such as a scatterometer is shown. It comprises a broadband (white light) radiation projector 2 which projects radiation 5 onto a substrate W. The reflected or scattered radiation 10 is passed to a spectrometer detector 4 which measures the spectrum 6 of the specularly reflected radiation 10 (i.e. a measure of the intensity I as a function of wavelength λ). From this data, the structure or profile 8 which gave rise to the detected spectrum can be reconstructed by a processing unit PU, for example by rigorous coupled wave analysis and non-linear regression or by comparison with a library of simulated spectra. Typically, for the reconstruction, the general form of the structure is known and some parameters are assumed based on knowledge of the process by which the structure was manufactured, leaving only a few parameters of the structure to be determined from the scatterometry data. Such a scatterometer can be configured as a normal incidence scatterometer or an oblique incidence scatterometer.

[0049] In a first embodiment, the scatterometer MT is an angle-resolved scatterometer. In such a scatterometer, a reconstruction method can be applied to the measurement signal to reconstruct or calculate the properties of the grating. For example, such a reconstruction can be obtained by simulating the interaction of the scattered radiation with a mathematical model of the target structure and comparing the simulation results with the measurement results. The parameters of the mathematical model are adjusted until the simulated interaction produces a diffraction pattern similar to that observed from a real target.

[0050] In a second embodiment, the scatterometer MT is a spectroscopic scatterometer MT. In such a spectroscopic scatterometer MT, radiation emitted by a radiation source is directed onto a target and reflected or scattered radiation from the target is directed to a spectrometer detector which measures the spectrum of the specularly reflected radiation (i.e. a measure of the intensity as a function of wavelength). From this data, the structure or profile of the target which produced the detected spectrum can be reconstructed, for example by rigorous coupled wave analysis and nonlinear regression or by comparison with a library of simulated spectra.

[0051] In a third embodiment, the scatterometer MT is an ellipsometric scatterometer. An ellipsometric scatterometer allows the parameters of a lithographic process to be determined by measuring the scattered radiation in each polarization state. Such a measurement device emits polarized light (e.g. linear, circular or elliptical) by using, for example, an appropriate polarization filter in the illumination portion of the measurement device. A source suitable for the measurement device may also provide polarized radiation. Various embodiments of prior art ellipsometric scatterometers are described in U.S. patent applications 11 / 451,599, 11 / 708,678, 12 / 256,780, 12 / 486,449, 12 / 920,968, 12 / 922,587, 13 / 000,229, 13 / 033,135, 13 / 533,110 and 13 / 891,410, the entire contents of which are hereby incorporated herein by reference.

[0052] In one embodiment of the scatterometer MT, the scatterometer MT is adapted to measure the overlay of two misaligned gratings or periodic structures by measuring the reflection spectrum and / or an asymmetry in the detection configuration, the asymmetry being related to the degree of overlay. The two (usually overlaid) grating structures may be applied in two different layers (not necessarily continuous layers) and may be formed substantially at the same location on the wafer. The scatterometer may have a symmetrical detection structure, such as described in co-owned patent application EP1,628,164A, so that any asymmetry can be clearly distinguished. This provides a direct method of measuring misalignment in the gratings. Other examples of overlay errors between two layers containing periodic structures when measuring the target by the asymmetry of the periodic structure may be found in PCT patent application publication number WO2011 / 012624 or in US patent application US20160161863, the entire contents of which are incorporated herein by reference.

[0053] Other parameters of interest may be focus and dose. Focus and dose may be determined simultaneously by scatterometry (or, alternatively, by scanning electron microscopy), as described in U.S. Patent Application US20110249244, the entire contents of which are incorporated herein by reference. A single structure may be used that has a unique combination of critical dimension and sidewall angle measurements for each point in the Focus Energy Matrix (FEM - also called Focus Exposure Matrix). If these unique combinations of critical dimension and sidewall angle are available, then focus and dose values ​​may be uniquely determined from these measurements.

[0054] The metrology target can be a collection of composite gratings formed by a lithography process (mainly in resist, but also after, for example, an etching process). Typically, the pitch and line width of the structures in the grating strongly depend on the measurement optics (particularly the NA of the optics) in order to be able to capture the diffraction orders from the metrology target. As mentioned before, the diffraction signal can be used to determine the offset between two layers (also called "overlay"), or can be used to reconstruct at least a portion of the original grating produced by the lithography process. This reconstruction can be used to provide guidance on the quality of the lithography process and can be used to control at least a portion of the lithography process. The target can have a smaller sub-division, which is configured to mimic the size of a functional part of the design layout in the target. Due to this sub-division, the target will behave more similar to the functional part of the design layout, so that the overall process parameter measurement better resembles the functional part of the design layout. The target can be measured in an underfill mode or in an overfill mode. In the underfill mode, the measurement beam produces a spot that is smaller than the entire target. In the overfill mode, the measurement beam produces a spot that is larger than the entire target. In this overfill mode, it is also possible to measure different targets simultaneously, thereby determining different process parameters simultaneously.

[0055] The overall measurement quality of a lithography parameter using a particular target is determined at least in part by the measurement recipe used to measure the lithography parameter. The term "substrate measurement recipe" may include: one or more parameters of the measurement itself, one or more parameters of one or more patterns measured, or both. For example, if the measurement used in the substrate measurement recipe is a diffraction-based optical measurement, the one or more parameters measured may include the wavelength of the radiation, the polarization of the radiation, the angle of incidence of the radiation relative to the substrate, the orientation of the radiation relative to the pattern on the substrate, and the like. One of the criteria for selecting a measurement recipe may, for example, be the sensitivity of one of the measurement parameters to process variations. More examples are described in U.S. patent application US20160161863 and published U.S. patent application US2016 / 0370717A1, which are incorporated herein by reference in their entirety.

[0056] A metrology device using a computational imaging / phase acquisition method is described in U.S. Patent Publication US2019 / 0107781, which is incorporated herein by reference. Such a metrology device can use relatively simple sensor optics, which have no exceptional or even relatively ordinary aberration performance. In this way, the sensor optics can be allowed to have aberrations and thus produce relatively aberrated images. Of course, simply allowing larger aberrations in the sensor optics will have an unacceptable impact on image quality unless something is done to compensate for the effects of these optical aberrations. Therefore, computational imaging techniques are used to compensate for the negative effects of relaxation in aberration performance in the sensor optics.

[0057] In this method, the intensity and phase of the target are retrieved from one or more intensity measurements of the target. Phase acquisition can use a priori information of the measurement target (for example, for inclusion in the loss function that forms the starting point of the derived / designed phase acquisition algorithm). Alternatively, or in combination with existing information methods, diversity measurements can be performed. In order to achieve diversity, the imaging system is slightly changed between measurements. An example of diversity measurement is by focus stepping, that is, by obtaining measurements at different focus positions. Alternative methods for introducing diversity include, for example, using different illumination wavelengths or different wavelength ranges, modulating illumination, or changing the incident angle of illumination on the target between measurements. Phase acquisition itself can be based on the phase acquisition described in the aforementioned US2019 / 0107781 or patent application EP 17199764 (also incorporated herein by reference). This describes determining the corresponding phase acquisition based on the intensity measurement, so that the interaction between the target and the illuminating radiation is described according to its electric field or complex domain ("complex" here means that there is amplitude and phase information). The quality of the intensity measurement may be lower than that used in conventional measurements, and therefore may be out of focus as described. The described interaction may include a representation of the electric and / or magnetic fields immediately above the target. In such an embodiment, the electric and / or magnetic field images of the illuminated target are modeled as an equivalent source description by infinitesimal electric and / or magnetic current dipoles on a surface in a plane (e.g., two-dimensional) parallel to the target. Such a plane may, for example, be a plane immediately above the target, such as a plane that is in focus according to the Rayleigh criterion, although the location of the model plane is not critical: once the amplitude and phase on one plane are known, they can be computationally generalized to any other plane (focus plane, defocus plane, or even pupil plane). Alternatively, the description may include the complex transmission of the target or its two-dimensional equivalent.

[0058] The phase acquisition may include modeling the effect of the interaction between the illuminating radiation and the target on the diffracted radiation to obtain a modeled intensity pattern; and optimizing the phase and amplitude of the electric field / complex field within the model so as to minimize the difference between the modeled intensity pattern and the detected intensity pattern. More specifically, during measurement acquisition, an image (e.g., an image of the target) is captured on a detector (at a detection plane) and its intensity is measured. A phase acquisition algorithm is used to determine the amplitude and phase of the electric field at a plane parallel to the target (e.g., immediately above the target). The phase acquisition algorithm uses a forward model of the sensor (e.g., taking into account aberrations) to perform computational imaging of the target to obtain model values ​​of the intensity and phase of the field at the detection plane. No target model is required. The difference between the modeled intensity value and the detected intensity value is minimized (e.g., iteratively) in terms of phase and amplitude, and the corresponding modeled phase value obtained is considered to be the phase detected. A specific method for using complex fields in measurement applications is described in PCT application PCT / EP2019 / 052658, which is also incorporated herein by reference.

[0059] Such an iterative algorithm is computationally expensive and therefore takes a long time to converge to a solution, and there is no guarantee when it will do so, or that the solution is optimal. Therefore, a number of non-iterative methods for determining the complex field from the intensity image will be described. Furthermore, there are inherent assumptions in using focus diversity measurements, such as the assumption that moving the sample through the focus is equivalent to moving the detector through the focus, the validity of which is questionable. Thus, the methods described herein (which additionally include iteratively calculated complex field embodiments) eliminate the need for such through-focus diversity measurements.

[0060] The methods described herein include obtaining a plurality of different images for which one or more changes have been made between images in a Fourier plane (or pupil plane) of radiation reflected by a sample (e.g., a target). By applying appropriate (amplitude and / or phase) modulation in the Fourier plane (e.g., using a modulator or mask), a sequence of images can be captured in the image plane from which a complex-valued field can be non-iteratively reconstructed.

[0061] Figure 5A basic arrangement that can be used for many of the embodiments described herein is shown. It shows a sample S or target in a sample plane SP. The radiation field reflected from the sample S passes through an imaging lens (or imaging system) L and a beam splitter BS to a mask M or amplitude modulator in a Fourier plane FP. The mask M changes or modulates the amplitude of the Fourier transform of the field reflected by the sample S (the Fourier transformed reflected field). A first detector IDET or camera at the image plane IM detects an image of the field reflected by the sample after it has been Fourier filtered by the mask M. An optional second detector or camera FDET can be located at the Fourier plane FP for imaging the intensity Fourier transform of the field reflected by the sample before being modulated by the mask M.

[0062] The second detector FDET and the associated Fourier imaging branch (and hence the beam splitter BS) are optional. They are used in applications such as Figure 6 It is useful in the illustrated embodiments (as described below) for which specific mask properties or modulations should ideally be applied in specific regions of the Fourier transform of the field. Thus, the image recorded in the Fourier plane by the second detector FDET can help determine which amplitude modulations should be applied. Additionally or alternatively, such an image can be used as additional information to improve the reconstruction using an iterative phase acquisition algorithm.

[0063] Figure 6 An embodiment is shown in which a plurality of matched mask pairs M1, M1 P Applied to the Fourier transformed reflected field FT, each mask of a pair differs from each other only in the (e.g. small) perturbation region P. For example, the masking can be implemented by providing each pair of masks with two differently modulated (e.g. digital) binary amplitude modulators (e.g. digital micromirror devices DMD).

[0064] The reflected field from the sample consists of a sample amplitude component A and an (unknown) sample phase component The Fourier transformed reflected field FT is the field incident on the mask / binary amplitude modulator (and Fourier detector FDET, if present) in the Fourier plane FP of the imaging lens L, which is modulated using the first mask of the matching mask pair (i.e., the unperturbed mask M1). The image Im1 in the image plane resulting from the Fourier modulated field is captured and recorded (e.g., by the image plane detector IDET). Then, the second mask of the matching mask pair, i.e., the perturbed mask M1 P , is used to modulate the Fourier transformed reflected field FT, and the resulting image Im2 in the image plane is captured and recorded (eg, by an image plane detector IDET). Fourier transform FT M1'The reconstructed portion of can be reconstructed based on the difference of the inverse Fourier transform of each of the two recorded images Im1, Im2.

[0065] In one embodiment, two different modulation functions M1, M1 are applied by a binary amplitude modulator. P (i.e., mask M is implemented using a binary amplitude modulator). In the brighter regions R1, the radiation is reflected (or transmitted depending on the setting) without being altered, while in the darker regions R2, the amplitude is set to zero. The difference between the two modulation functions is a small perturbation region P where the amplitude is modulated in one mask but not in the other. In one embodiment, the small perturbation may essentially consist of a "pinhole" that reflects the perturbation mask M1. P The perturbed regions should be at the borders of the reconstruction regions R1 (e.g., the reflection regions). Furthermore, the perturbed regions should be at locations where the amplitude of the Fourier transform is high so that the reconstruction scheme is noise robust. Camera FDET in the Fourier plane of the imaging lens can be used to help identify such regions.

[0066] These steps are repeated for many other mask pairs M2-M8 (ie, each mask pair has a corresponding perturbation mask M2 P -M8 P , not shown) are repeated, the reflection region is moved around these masks so as to cover the entire Fourier transformed reflection field FT (eg, except for the perturbation region, which is for the perturbation mask M1 P -M8 P are common). By taking the obtained reconstructed part FT M1 '-FT M8 '(Only FT is shown M1 ') together (e.g., stitched together), it is possible to non-iteratively reconstruct almost the entire Fourier transform FT' (i.e., all but the perturbed region P). Inverse Fourier transforming the result yields the complex-valued field reflected by the sample The more mask pairs used, the more robust the measurement will be. However, it is obvious that the full field can be reconstructed with only four mask pairs, for example, M1, M4, M5 and M6 (together with their perturbed counterparts), as long as at least two of these masks have a slightly larger reflection area.

[0067] Therefore, the reconstruction method can be described as a self-referencing holographic method, more details of which can be found in the publication: Shao et al., “Spatial coherence measurement and partially coherent diffractive imaging using self-referencing holography,” Opt. Express 26, 4479-4490 (2018), which is incorporated herein by reference.

[0068] In principle, the reconstruction region can be made larger in order to reduce the number of measurements required. Figure 7 shows a system having two pairs of masks M9, M9 P and M10, M10 P However, using these may increase the noise sensitivity of the scheme, since the total field in the perturbed region should be strong compared to the total field in the reconstructed region, and may make the final refinement with the iterative algorithm less reliable, since there is less redundancy in the measurements.

[0069] Note that the final reconstruction is not perfect because the Fourier transform is not reconstructed in the disturbed region (where the amplitude is typically high). There are many ways to solve this problem. In a first example, the image recorded by the Fourier camera FDET in the Fourier plane of the imaging lens can be used to infer the amplitude in the disturbed region. Alternatively, the above non-iterative reconstruction scheme can be performed for at least two different disturbed regions, one of which is used to complete the other. As another alternative, an iterative algorithm can be used to improve the reconstruction. The data set used for non-iterative reconstruction also allows reconstruction using Fourier stack imaging. The fact that a good initial guess is available (e.g., inferred from the Fourier camera FDET) should avoid the problems of non-convergence and high computational overhead.

[0070] The mask may include a phase modulator instead of a binary amplitude modulator. In such an embodiment, reconstruction can be performed by applying three phase shifts in the perturbed region (this is called phase-shifting holography / interferometry, also known as quantitative Zernike phase contrast microscopy, see P. Gao et al., “Phase-shifting Zernike phase contrast microscopy for quantitative phase measurement,” Opt. Lett. 36, 4305-4307 (2011), which is incorporated herein by reference). In this case, the perturbed region does not have to be at the edge of the reconstruction region, but can be within the reconstruction region. Therefore, there will be no need to perform multiple non-iterative reconstructions of different regions that need to be stitched together. Disadvantages may include that phase modulators are more expensive than amplitude modulators and are independent of wavelength.

[0071] Figure 8 Another alternative is shown, in which the mask comprises a mechanically movable mask RM, such as a rotating mask. Such a mask does not suffer from pixelation. Furthermore, because such a mask is transmissive, the beam does not need to pass through a beam splitter BS additionally, thereby reducing intensity losses. However, such an embodiment does introduce mechanical movement. The mask RM can be a rotating mask, comprising a selective (e.g., openable and closable) perturbation region P. In one example, the perturbation region P coincides with the axis of rotation of the rotating mask RM.

[0072] Reference Fig. 9 A number of other embodiments are described with reference to the simplified arrangement schematically shown in . This shows a sample S at a sample plane SP, an imaging lens L, a mask M and a detector DET at an image plane IP. Each of these embodiments may have the pupil / Fourier plane imaging branch already described.

[0073] Fig.10 An embodiment is shown in which the mask M comprises a grating G with a reference pinhole RP. The sample S is illuminated with a spot of finite size. The field reflected by the sample is imaged by an imaging lens L. The amplitude grating G with the reference pinhole RP is placed in the Fourier plane FP of the lens L. The reference pinhole RP should be located where the field amplitude is high. A detector or camera DET at the image plane IP of the imaging lens L detects the multiple diffraction orders generated by the grating G within a single image.

[0074] There are two ways to interpret the reconstruction method. One way is to view it as an example of Fourier transform holography. Another way is to view it as an example of phase-shift holography, where a grating is used to simultaneously generate multiple interference patterns. In the Fourier transform holographic interpretation, a binary amplitude grating has a certain support. The support of the grating and the position of the reference pinhole are such that the autocorrelations of the mask comprise a direct reconstruction of the grating; thus, it is simple to extract the grating reconstruction from the mask autocorrelations (i.e., where the mask autocorrelations are obtained by Fourier transforming the intensity image). More details of this method of reconstructing a complex-valued field using this approach can be found in Lu et al.: “Noniterative spatially partially coherent diffractive imaging using pinhole array mask”, Advanced Photonics, 1(1), 016005 (2019), which is incorporated herein by reference. In the parallel phase-shift holographic interpretation, the reference pinhole generates a reference plane wave in the image plane that interferes with the image field. In order for phase-shift holography to work, the phase of this reference plane wave must be shifted relative to the image field. By introducing a grating, copies of the image field (ie diffraction orders) are generated with different phases relative to a reference plane wave. Thus, by measuring multiple diffraction orders in a single measurement, single-shot reconstruction is possible.

[0075] Thus, a single measurement and a single Fourier transform are sufficient for reconstruction and no mechanical movement of the components is required.However, a camera with a significantly larger field of view is required compared to many of the other embodiments described herein.

[0076] Fig.11 Another self-referencing holographic embodiment is shown, which can use a binary amplitude modulator in the Fourier plane of the imaging lens (e.g., Fig. 9 The mask M in the embodiment comprises a binary amplitude modulator). In this embodiment, three regions A1, A2 and B are defined in the Fourier plane FP. The non-iterative phase acquisition method comprises several steps.

[0077] In the first step, a mask M11 (or two masks M11, M11', to improve robustness) is used to reconstruct the field in the region B by Fourier transform holography. The darker areas represent blocked areas, and the brighter areas represent transmitted areas, where the transmitted areas include an area B' corresponding to the reconstructed area B defined in the Fourier plane and a plurality of reference points RP.

[0078] Two measurements are then made: a first measurement in which the field in area A1+B is transmitted by the mask, and a second measurement in which only the field in area A1 is transmitted. From these two measurements, it is possible to directly extract the convolution of the field in area A1 with the field in area B. This can be done using the same techniques as those already described for Figure 6 The method of implementing the method described in the embodiment ...

[0079] Then, a third measurement of the position where the field in area A2+B is transmitted by the mask is performed, and a fourth measurement of the position where only the field in area A2 is transmitted, and the same process is performed to reconstruct the field in area A2. The reconstructions of the fields in areas A1, A2 and B can then be combined to reconstruct the complete field in the Fourier plane. Due to the finite size of the reference point RP and the finite width of area B, the quality of the reconstruction is degraded. Therefore, a final refinement using iterative phase acquisition can be performed.

[0080] and Figure 6 and Fig.10 The advantage of this embodiment over the embodiment shown is that it does not rely on a single reference point where the amplitude is assumed to be high. Instead, it is assumed that there is at least one point with high amplitude somewhere in region B, which is true for the sample of interest. Therefore, the mask does not need to be shifted to different positions for different samples.

[0081] In one embodiment, it is also possible to implement double blind Fourier holography, as described in O. Raz et al., "Direct phase retrieval in double blind Fourier holography," Opt. Express 22, 24935-24950 (2014), which is incorporated herein by reference. In this case, only three measurements are required, each using Fig.12 One of the three masks M12, M13, M14 shown. From the three corresponding measurements, a system of linear equations can be constructed and solved non-iteratively. However, because each system is quite large and there are many systems (if the camera has N×N pixels, there will be 2N systems), the computation time will be significantly higher than the method proposed above, unless the 2N systems can be solved in parallel.

[0082] Another hybrid phase acquisition method will now be described which illustrates the similarity with any of the self-referencing holographic embodiments described above (e.g., Figure 6 , Figure 7 , Figure 8 , Fig.10 or Fig.11 ). That embodiment and this embodiment both solve the so-called "twin problem". The twin problem is a problem in which the spatial content of an image includes two terms in linear imaging (for completeness, there is a third term for nonlinear imaging that will be discussed later in the so-called effective linearization of the imaging process), where one of the linear imaging terms is called a regular image (more specifically, a regular field) and the other of the linear terms is called a twin image (more specifically, a twin field) because it involves a point-inverted object wavefield. Therefore, mathematically, there are the following two linear terms (for simplicity, the primary (first) spatial frequency is assumed here to propagate along the optical axis of the lens) that contribute to the same image intensity represented by I(+G) (in Fourier space, G is a 2D spatial frequency vector in Fourier space):

[0083] Regular image terms: Fourier coefficients involving the object represented by O(+G) (where O is the (complex-valued) Fourier transform of the object field, and G is the 2D spatial frequency vector in Fourier space of the exit pupil); and

[0084] · Twin image term: refers to the Fourier coefficients of the object represented by O*(-G) (where * represents complex conjugation).

[0085] In this embodiment, a more limited selection of apertures is proposed, rather than Figure 6 , Figure 7 Figure 8 , Fig.10 or Fig.11 The aperture arrangement described; a more limited aperture selection only affects the presence / omission of the first diffraction order in the imaging process. This aperture selection results in a first image with a selected higher diffraction order (e.g., the first diffraction order) and a second image (otherwise similar) without the selected higher diffraction order. Subtracting the second image from the first image prior to phase acquisition results in an effective linearization of the imaging process. When combined with focus variation, this linearization enables a direct non-iterative phase acquisition process, which also solves the twin problem (with Fig.11 The twinning problem is still a problem due to the limited aperture choice compared to the finer aperture selection shown that directly solves the twinning problem). It also ensures that a large portion of the exit pupil is used for imaging, as opposed to only about half or less in the self-referencing holography embodiments described earlier, thereby improving robustness to shot noise.

[0086] Fig.13 The basic imaging technology according to the exemplary embodiment is shown. The first Fourier plane of the device is denoted FP1 and the second image is used to illustrate the acquisition (where z is the focus setting), which together constitute a first image pair. In the first Fourier plane representation, a selected higher diffraction order peak (e.g., the first diffraction order peak) is not blocked, while in the second Fourier plane representation, the selected higher / first diffraction order peak is blocked. It is proposed to obtain multiple image pairs, for example, with a thru-focus sequence with one pair per focus setting z, wherein a difference is calculated for each of these image pairs; this achieves the effective linearization mentioned above.

[0087] For selectively blocking the first diffraction order in the Fourier plane (e.g. by Fig. 9 Any suitable arrangement of appropriately configured masks M15a or amplitude modulators as shown while having minimal effect on the rest of the pupil may be used for this embodiment. In the specific example shown, there are two diagonally or obliquely oriented elongated shields M15a, M15b that can be moved toward and away from each other to selectively block the first diffraction order (centered in the Fourier plane). The orientation of the shields should be oblique (e.g., at 45 degrees) relative to the diffraction pattern so as to minimize the blocking of diffracted radiation beyond the selectively blocked first diffraction order when configured as shield M15b.

[0088] First Image will include linear and nonlinear terms, and the second image Only nonlinear terms should be included. Mathematically expressed as:

[0089]

[0090] where G is the 2D coordinate in the exit pupil (spatial frequency in the Fourier plane), G1 is the 2D coordinate of the first diffraction order in the exit pupil, φ is the complex field of the target in the Fourier plane and p z is the phase transfer function in the Fourier plane.

[0091] Therefore, the difference between the two images ΔI z Only linear terms should be included:

[0092]

[0093] Therefore, the complex-valued field can then be obtained as a simple fitting problem, resulting in two linear equations. z The linearized image intensity described by (G) includes the sum of the twin image and the regular image:

[0094]

[0095]

[0096] where x, y comprise two unknowns. The focus diversity in the through-focus sequence enables separation of the twin image from the regular image (and thus solves the twin problem), for example, by solving a simple linear least squares fit of the two unknowns x, y:

[0097] ΔI z =x px z +y py z for z∈{z1,z2,...,z N}

[0098] Using the obtained x, that is, x = φ(G+G1)φ * (G1), the next step is to obtain φ * (G1) to obtain the complex-valued field φ(G+G1). * (G1) can be freely chosen to have zero phase. Denoting this amplitude as B, for each defocus value z, it can be obtained via the image pair and The amplitude is determined by the DC component of the two images, because:

[0099]

[0100] It should be noted that this value of B may preferably be determined in each phase acquisition step (eg, for two illumination settings resulting in +1st order and -1st order dark-field imaging).

[0101] The partially self-referenced holography methods described herein that rely on a pinhole (perturbation region) for reference (e.g., Figure 6 , Figure 7 , Figure 8 and Fig.10Another problem with the use of optical microscopes (those described in detail above) is that for different samples the mask may need to be shifted to different positions, since the pinhole needs to be located at a point where the field strength is high. If different samples have targets of different pitches, there will be a shift of points in the field with high intensity. To solve this problem, an alternative measurement arrangement is proposed which uses the zeroth order from the scattered radiation (i.e. the specularly reflected radiation from the sample) as a reference.

[0102] Fig.14 (a) schematically shows an arrangement for implementing zero-order self-referenced holography. A point source (e.g., an illumination pinhole PH) is imaged onto the pupil plane of a first lens L1 (e.g., an objective lens) through one or more input lenses IL. The first lens L1 focuses the illumination beam IB onto a sample T on a substrate W and captures the reflected zeroth order 0th (solid line) and at least one higher diffraction order 1st order (e.g., + / -1st order—dashed line). The second lens L2 produces an intermediate image at an intermediate image plane IIP. The intermediate image is re-imaged using a (e.g., single) third lens L3. A mask M including a mask pinhole PH' is located at the Fourier plane FP of lens L3. The position of the mask pinhole PH' coincides with the zeroth order 0th. As before, two images are captured: one with an open mask pinhole PH' and one with a blocked mask pinhole PH'. Alternatively, if the field at the mask pinhole PH' does not produce a uniform plane wave at the detector DET, a third image may be taken comprising only the field transmitted by the mask pinhole PH'.

[0103] The mask M may include holes that pass substantially the entire field (including the entire first diffraction order) rather than selectively opening and closing the mask pinhole PH (which is located at a fixed position coinciding with the zero-order position in the Fourier plane). Fig.10 In the embodiment of the present invention, using the zeroth order as a reference means that the pinholes can be located at the edge of the grating G, rather than inside it. However, if the pinhole at the zeroth order is far enough away from the reconstruction region at the first order, then no grating is required, as regular single-shot Fourier transform holography can be applied using the method of the present embodiment.

[0104] The refactoring method can again include something similar to what has already been discussed Figure 6 The methods described in the embodiments described in (e.g., subtracting the two measurements and inverse Fourier transforming the result, and cropping the twin image). If the pinhole does not produce a uniform plane wave (due to the finite size of the pinhole), the optional third image can be used to correct for this by Fourier transforming the reconstructed image (to go from the pupil plane to the image plane) and dividing the result by the square root of the third measurement.

[0105] In one embodiment, the pinhole may be apodized to produce a smoother reference beam.

[0106] Using the same lens for illumination and detection means that a stronger illumination beam must pass through the optical system on its way to the substrate. Any internal reflection or scattering from the surface results in stray light, which can cause imaging errors, especially when the diffraction from the target is weak.

[0107] Fig.14 (b) and (c) show a simplified arrangement of the objective lens arrangement by using a separate first lens L1' instead of Fig.14 The first lens (objective lens) L1 in (a) is used to mitigate double reflection and scattering. The separated first lens L1' includes a gap LG that divides the first lens L1 into three lens parts LP1, LP2, LP3. The gap LG should be large enough to prevent optical coupling between the lens parts LP1, LP2, LP3. In this article, large enough can be significantly larger than the wavelength of light (for example, 100λ). The gap LG can be optionally filled with an absorbing material. The use of a single lens for illumination and detection ensures that the imaging conditions are met and the zeroth order and the first order are path length matched.

[0108] The first lens section LP1 is used to focus the illumination beam 1B onto the sample T, the second lens section LP2 is used to capture the higher diffraction order 1st, and the third lens section LP3 is used to capture the specularly reflected zeroth order 0th. A filtering pinhole FPH can be provided to spatially filter the 0th order 0th reference beam. The zeroth and first order beams will then be reflected by the second lens L2 ( Fig.14 Note that the concept of a separate lens may be used in other embodiments described above, although such a lens may only include a first lens portion (for the illumination beam) and a second portion (for the diffraction orders), since the zeroth order is typically not captured.

[0109] In this arrangement (optionally), the use of a beam splitter BS is also avoided by directly using the fiber tip of the illumination fiber IF as a point light source placed at the pupil plane of the separated first lens L1 '. This makes the system compact and light efficient compared to the use of a beam splitter. However, this is at the expense of the overlay now being able to be measured only in wafer rotation mode.

[0110] The advantage of this zero-order self-referenced holography approach is that the mask no longer needs to be shifted. By placing the pinhole to coincide with the zero order while reconstructing the higher orders (e.g., +1 or -1), a strong reference wave is ensured, and the position of the pinhole can be the same for different samples (since the position of the zero order is fixed). Furthermore, only one reconstruction needs to be done, since the reconstruction is only for one side of the pinhole: in contrast, Figure 6The arrangement requires stitching together different reconstruction areas, each of which is reconstructed separately. However, the system will now have a reduced NA, since part of the NA is used for illumination and part for capturing the zeroth order. Furthermore, the stray light risk is still higher: the fact that the illumination beam and the zeroth order (both of high intensity) have to pass through the objective increases the risk of stray light interfering with the imaging process (although this can be mitigated by using separate lenses as described).

[0111] Another self-referenced holography approach can use binary holograms or Lee holograms to perform single-shot phase acquisition via phase-shift holography without the need for fast Fourier transform calculations.

[0112] Fig.15 is a schematic representation of a simplified arrangement of such an embodiment. The sample S is illuminated by an illumination radiation IR incident at an angle relative to the sample surface. The scattered radiation SR from the sample surface is collected by a first lens L1 (e.g., an objective lens of a measurement device) and subsequently imaged onto a first image plane IP1 by a second lens L2 (e.g., a tube lens). The aperture AP is used to truncate the image of the sample at the first image plane IP1, thereby preventing overlap of the three captured images. It should be noted that the aperture can be omitted if the arrangement and sample / illumination parameters are such that the images are separated in any case and are not included. The (truncated) first image is then re-imaged onto a detection plane where a detector DET (e.g., a CCD camera) is located by a third lens L3. A modulator M, which may include a spatial light modulator (SLM) and more specifically a digital micromirror device (DMD), is placed at the Fourier plane of the third lens L3. A DMD is a micro-electromechanical system device comprising a plurality (e.g., millions) of tiny switchable mirrors. Such tiny mirrors can have micrometer-scale dimensions, and each mirror (or pixel) can be controlled / switched individually. DMDs have been successfully applied to shape laser beams and generate various transverse laser modes, such as Laguerre-Gaussian beams, Ince-Gaussian modes, and cylindrically symmetric vector vortex beams. The modulator M applies a binary modulation to the scattered radiation at the Fourier plane.

[0113] According to an embodiment, the pattern imparted by the modulator M may be a binary hologram representation of a complex field modulation of the optical phase and amplitude, such as a Lee hologram. In the case where the modulator comprises a DMD, since the DMD can only apply binary amplitude modulation, two conversion steps may be employed. The first step may comprise converting the desired complex valued modulation into an expression according to the positive real valued Lee hologram F(x), namely:

[0114] F(x)=C+H(x)e ivx +H(x) * e-ivx

[0115] where H(x) is the expected complex-valued modulation of the complex-valued Lee hologram, and e ivx Define carrier. The positive real-valued Lee hologram, ie, F(x) of equation (1), can then be converted into a binary hologram, for example by dithering the positive real-valued Lee hologram F(x).

[0116] The result of the positive real-valued modulation F(x) in the Fourier plane of the illuminating radiation is the generation of three orders C, H(x), H(x) * , which are spatially separated at the detection plane; each of which corresponds to a respective coefficient of the three terms of the above F(x) equation. For example, the three spatially separated radiation beams include: 1) an unmodulated beam corresponding to a constant coefficient C; 2) a first modulated beam corresponding to a modulation coefficient H(x); and 3) a second modulated beam corresponding to a modulation coefficient H(x)*.

[0117] By choosing appropriate values ​​of H(x), for example to include a 2 / 3π phase shift relative to a reference point x0, the three orders measured at the detector plane will correspond to the images required for phase-shifting interferometry: namely, the field of an interfering plane wave that is phase-shifted by -2 / 3π, 0, and 2 / 3π radians for each beam, respectively. The complex-valued field can be recovered simply by taking a linear combination of these three images.

[0118] It should be noted that other choices of H(x) can be applied to obtain different kinds of diversity for phase acquisition. For example, if H(x) is chosen as a quadratic phase profile, it is possible to measure three through focus images that can be used for iterative phase acquisition in a single shot.

[0119] The advantages of this method are that the DMD is fast, can operate over a wide wavelength range, and does not require mechanical motion. Moreover, phase acquisition only requires a single shot and does not require FFT. Another advantage is that a modulation device (e.g., DMD) can perform phase acquisition and aberration correction simultaneously. By controlling the DMD to apply an aberration correction function (e.g., based on pre-characterization of the optical aberrations of the measurement system or based on an optimization method for monitoring image quality while changing the applied correction until optimized), the first modulated radiation beam H(x) will include an aberration-corrected image.

[0120] Fig.16An embodiment of Fourier ptychographic phase acquisition using a rotating pinhole mask M15 comprising a plurality of pinholes PH is shown. The pinhole mask M16 rotates in the Fourier plane with its axis of rotation outside the beam path. This introduces a series of known amplitude modulations that will be used in Fourier ptychographic phase acquisition of the reconstruction region RR (the darker shaded region). Fourier ptychographic is a known method (although it is usually implemented in different ways), see, for example, G. Zheng et al., "wide-field, high-resolution Fourier ptychographic microscopy". Nature photonics 7.9 (2013): 739 (incorporated herein by reference).

[0121] Such a mask ensures a robust reconstruction, since each pinhole imposes a strong localization constraint. If a high intensity is detected in the image plane, it can be assumed that it must come from the restricted area defined by the pinhole. By moving the pinhole back and forth to obtain a sequence of images with different pinhole positions (the mask M16' is the same mask that has been rotated), the reconstruction becomes almost a combinatorial problem: in each image, it can be assumed that the detection of high intensities comes from the area corresponding to the pinhole (the pinhole position is known). Therefore, if a set of measurements all include high intensities, it is possible to determine the area covered by the pinhole common to all these images, which must be the source of the detected energy. In contrast, applying a focus variation results in applying a phase modulation in the Fourier plane, which does not give such a localization constraint.

[0122] Thus, the reconstruction method may include iteratively minimizing the difference between the estimated image amplitude (computed from the estimated field in the Fourier plane constrained by the known modulation (ie, the pinhole position)) and the measured image amplitude.

[0123] The phase is determined iteratively in this embodiment (unlike other embodiments), but it is expected that the number of iterations required for the phase acquisition algorithm will be significantly less (e.g., in the range of 10 times) compared to focus diversity based approaches.

[0124] Fig.171 is a block diagram illustrating a computer system 1600 that can help implement the methods and processes disclosed herein. The computer system 1600 includes a bus 1602 or other communication mechanism for transmitting information, and a processor 1604 (or multiple processors 1604 and 1605) coupled to the bus 1602 for processing information. The computer system 1600 also includes a main memory 1606, such as a random access memory (RAM) or other dynamic storage device, coupled to the bus 1602 for storing information and instructions to be executed by the processor 1604. The main memory 1606 can also be used to store temporary variables or other intermediate information during the execution of instructions by the processor 1604. The computer system 1600 also includes a read-only memory (ROM) 1608 or other static storage device coupled to the bus 1602 for storing static information and instructions for the processor 1604. A storage device 1610, such as a magnetic disk or optical disk, is provided and coupled to the bus 1602 for storing information and instructions.

[0125] The computer system 1600 may be coupled via the bus 1602 to a display 1612, such as a cathode ray tube (CRT) or a flat panel or touch panel display, for displaying information to a computer user. An input device 1614, including alphanumeric and other keys, is coupled to the bus 1602 for communicating information and command selections to the processor 1604. Another type of user input device is a cursor controller 1616, such as a mouse, a trackball, or cursor direction keys, for communicating direction information and command selections to the processor 1604, and for controlling cursor movement on the display 1612. The input device typically has two degrees of freedom in two axes, a first axis (e.g., x) and a second axis (e.g., y), which allows the device to specify a position in a plane. A touch panel (screen) display may also be used as an input device.

[0126] One or more methods described herein may be performed by computer system 1600 in response to processor 1604 executing one or more sequences of one or more instructions contained in main memory 1606. Such instructions may be read into main memory 1606 from another computer-readable medium such as storage device 1610. Execution of the sequences of instructions contained in main memory 1606 causes processor 1604 to perform the processing steps described herein. One or more processors in a multiprocessing device may also be used to execute the sequences of instructions contained in main memory 1606. In alternative embodiments, hardwired circuitry may be used in place of or in combination with software instructions. Therefore, the description herein is not limited to any specific combination of hardware circuitry and software.

[0127] The term "computer-readable medium" as used herein refers to any medium that participates in providing instructions to processor 1604 for execution. Such media may take many forms, including, but not limited to, non-volatile media, volatile media, and transmission media. Non-volatile media include, for example, optical or magnetic disks, such as storage device 1610. Volatile media include dynamic memory, such as main memory 1606. Transmission media include coaxial cables, copper wire, and optical fiber, including the wires that make up bus 1602. Transmission media may also take the form of acoustic or light waves, such as those generated during radio frequency (RF) and infrared (IR) data communications. Common forms of computer-readable media include, for example, floppy disks, flexible disks, hard disks, magnetic tape, any other magnetic medium, CD-ROMs, DVDs, any other optical medium, punch cards, paper tape, any other physical medium with a pattern of holes, RAM, PROMs and EPROMs, FLASH-EPROMs, any other memory chip or cartridge, a carrier wave as described below, or any other medium from which a computer can read.

[0128] Various forms of computer readable media may be involved in carrying one or more sequences of one or more instructions to processor 1604 for execution. For example, the instructions may initially be carried on a disk of a remote computer. The remote computer can load the instructions into its dynamic memory and send the instructions over a telephone line using a modem. A modem local to computer system 1600 can receive the data on the telephone line and use an infrared transmitter to convert the data to an infrared signal. An infrared detector coupled to bus 1602 can receive the data carried in the infrared signal and place the data on bus 1602. Bus 1602 transfers the data to main memory 1606, from which processor 1604 retrieves and executes the instructions. The instructions received by main memory 1606 may optionally be stored on storage device 1610 before or after execution by processor 1604.

[0129] The computer system 1600 also preferably includes a communication interface 1618 coupled to the bus 1602. The communication interface 1618 provides a two-way data communication coupled to a network link 1620 connected to a local network 1622. For example, the communication interface 1618 can be an integrated services digital network (ISDN) card or a modem to provide a data communication connection to a corresponding type of telephone line. As another example, the communication interface 1618 can be a local area network (LAN) card to provide a data communication connection to a compatible LAN. A wireless link can also be implemented. In any such implementation, the communication interface 1618 sends and receives electrical signals, electromagnetic signals, or optical signals that carry digital data streams representing various types of information.

[0130] The network link 1620 typically provides data communication to other data devices through one or more networks. For example, the network link 1620 may provide a connection to a host computer 1624 or to data equipment operated by an Internet Service Provider (ISP) 1626 through a local network 1622. The ISP 1626, in turn, provides data communication services through a global packet data communication network, now commonly referred to as the "Internet" 1628. Both the local network 1622 and the Internet 1628 use electrical, electromagnetic or optical signals that carry digital data streams. The signals through the various networks and the signals on the network link 1620 and the signals through the communication interface 1618 (which carry the digital data to and from the computer system 1600) are exemplary forms of carrier waves that transport the information.

[0131] The computer system 1600 can send messages and receive data, including program code, through the network, network link 1620, and communication interface 1618. In the Internet example, server 1630 can send the requested code of the application program through Internet 1628, ISP 1626, local network 1622, and communication interface 1618. For example, one such downloaded application can provide one or more of the techniques described herein. The received code can be executed by processor 1604 as it is received, and / or stored in storage device 1610 or other non-volatile storage device for later execution. In this way, computer system 1600 can obtain application program code in the form of a carrier wave.

[0132] Further embodiments are disclosed in the following numbered clauses:

[0133] 1. A method of determining a complex-valued field associated with a sample measured using an imaging system, comprising:

[0134] obtaining image data associated with a series of images of the sample imaged at an image plane of the imaging system, and applying at least two different modulation functions in a Fourier plane of the imaging system to the image data; and

[0135] A complex-valued field is determined from the imaging data based on the applied modulation function.

[0136] 2. The method of clause 1, wherein the at least two different modulation functions comprise a plurality of modulation function pairs, each modulation function pair comprising a modulation function that differs only in the perturbation region.

[0137] 3. A method according to clause 2, wherein each modulation function comprises a corresponding reconstruction region and a blocking region, the reconstruction region covering a different part of the Fourier plane for each different pair of modulation functions.

[0138] 4. A method according to clause 2 or 3, wherein the pair of modulation functions is implemented by a binary amplitude modulator.

[0139] 5. A method according to clause 2 or 3, wherein the pair of modulation functions is achieved by a moving mask having a selectively closed aperture for providing a difference in the modulation functions at the perturbed regions.

[0140] 6. The method of clause 5, wherein the moving mask is a rotating mask and the selectively closed aperture is located at the axis of rotation.

[0141] 7. The method of clause 2, wherein the pair of modulation functions is implemented by a phase modulator.

[0142] 8. The method of clause 7, wherein the disturbance region is located within the reconstruction region.

[0143] 9. A method according to any one of clauses 2 to 8, wherein the disturbance region is located at a high intensity region in the Fourier plane.

[0144] 10. A method as defined in any one of clauses 2 to 9, comprising the steps of:

[0145] determining a plurality of partially reconstructed Fourier transforms by inverse Fourier transforming the series of images and determining differences between results for pairs of images corresponding to each of the plurality of modulation function pairs;

[0146] combining the partially reconstructed Fourier transforms to obtain a reconstructed Fourier transform; and

[0147] The complex-valued field is determined from the reconstructed Fourier transform.

[0148] 11. A method as defined in any one of clauses 2 to 10, comprising the step of reconstructing the field at the disturbance zone by performing one or more of the following:

[0149] inferring the amplitude at the disturbance region from the corresponding image in the Fourier plane;

[0150] performing the method to reconstruct two or more disturbed regions and using one of the reconstructions to reconstruct the disturbed region of another;

[0151] The field at the perturbed region is iteratively reconstructed using Fourier stack imaging.

[0152] 12. A method according to clause 1, wherein the modulation function comprises an amplitude grating and a reference pinhole; and the method comprises:

[0153] capturing in a single image multiple diffraction orders diffracted by the grating; and

[0154] A complex-valued field is determined from the imaged multiple diffraction orders.

[0155] 13. A method according to clause 12, wherein the complex-valued field is determined from the imaging data using one of Fourier transform holography or parallel phase-shift holography.

[0156] 14. A method according to clause 12 or 13, wherein the reference pinhole is located at a high intensity region in the Fourier plane.

[0157] 15. The method of clause 1, comprising defining at least three regions in the Fourier plane: a first reconstruction region, a second region and a third region;

[0158] reconstructing the field for the first reconstruction area from the image data, the image data being obtained from at least a first modulation function that transmits or reflects only in the first reconstruction area and at a plurality of reference points;

[0159] The fields of the second and third regions are reconstructed by the following steps:

[0160] determining a first convolution of the fields of the first reconstruction area and the second area based on image data obtained from a second modulation function transmitted or reflected only in the first reconstruction area and the second area and a third modulation function transmitted or reflected only in the second area;

[0161] determining a second convolution of the fields of the first reconstruction area and the third area from image data obtained from a fourth modulation function transmitted or reflected only in the first reconstruction area and the third area and a fifth modulation function transmitted or reflected only in the third area;

[0162] deconvolving the first convolution using the reconstructed field for the first reconstruction region to reconstruct the field for the first region and deconvolving the second convolution to reconstruct the field for the second region;

[0163] The reconstructed fields of the first reconstruction region, the second region and the third region are combined to determine the complex-valued field.

[0164] 16. The method according to clause 1, comprising:

[0165] constructing a plurality of linear equation systems from the image data, the image data comprising at least a first image obtained from at least a first modulation function corresponding to a full field to be reconstructed, a second image obtained from a second modulation function corresponding to a first half of the full field, and a third image obtained from a third modulation function corresponding to a second half of the full field; and

[0166] The plurality of linear systems of equations are solved non-iteratively using double-blind Fourier holography.

[0167] 17. A method according to claim 1, wherein the at least two different modulation functions include a first modulation function for obtaining a first image of an image pair and a second modulation function for obtaining a second image of the image pair, and wherein the only substantial difference between the modulation functions is that the second modulation function blocks selected higher diffraction orders and the first modulation function does not block selected higher orders.

[0168] 18. A method as described in clause 17, wherein the first modulation function and the second modulation function each blocks less than 10% or 5% of an area defined by a Fourier plane.

[0169] 19. A method as described in clause 17 or 18, wherein the first modulation function and the second modulation function are configured to block a minimum amount of diffracted radiation, except for selected higher orders being blocked by the second modulation function.

[0170] 20. The method according to clause 17, 18 or 19, further comprising:

[0171] For each of the pairs of images a difference image between the first image and the second image is determined, each of the difference images describing the image solely in terms of linear imaging terms.

[0172] 21. A method according to clause 20, comprising capturing a plurality of said image pairs, each image pair being associated with one of a plurality of focus levels; and determining a difference image for each image pair to obtain a through-focus series of difference images; and

[0173] By performing a linear fit of two unknowns on the difference images of the through-focus series, the twin image is separated from the regular image in each of the determined difference images.

[0174] 22. The method of clause 1, wherein:

[0175] The two different modulation functions differ only in: the selective opening and closing of a reference pinhole defining a perturbation region aligned in the Fourier plane with the zeroth order of the reflected radiation from the sample; and

[0176] Said determining of the complex-valued field is performed by a self-referenced holographic method using said zero-order reference.

[0177] 23. A method according to clause 22, wherein each of the two different modulation functions passes substantially the full field of the Fourier plane, except that the perturbation region is blocked in only one of the two different modulation functions.

[0178] 24. A method according to clause 22 or 23, wherein the determining step comprises:

[0179] determining a difference between a first measurement corresponding to a first one of the two different modulation functions and a second image corresponding to a second one of the two different modulation functions; and

[0180] The result is inverse Fourier transformed to obtain the reconstructed complex field.

[0181] 25. The method of clause 24, wherein the determining step further comprises clipping the twin field from the reconstructed complex field.

[0182] 26. A method according to clause 24 or 25, further comprising obtaining a third measurement corresponding to a third modulation function that blocks the full field except for the disturbance region, and using the third measurement to correct the reconstructed complex field for the effects of the finite size of the disturbance region.

[0183] 27. The method according to any one of clauses 22 to 26, further comprising:

[0184] Focusing a point source onto the sample,

[0185] focusing the zeroth order and at least one higher diffraction order at an intermediate image plane; and

[0186] A modulation function is applied to the Fourier plane of the lens which re-images the intermediate image plane.

[0187] 28. A method according to any one of clauses 22 to 27, comprising using a separate objective lens to irradiate the sample and capture the zeroth radiation and at least one higher diffraction order; wherein the separate objective lens comprises a plurality of parts separated by gaps, the plurality of parts comprising a first part for focusing the irradiating radiation onto the sample, a second part for capturing at least one higher diffraction order and a third part for capturing the zeroth order.

[0188] 29. A method according to any of clauses 22 to 28, wherein the reference pinhole is apodized.

[0189] 30. A method according to any preceding clause, wherein for a majority of the complex-valued fields, the step of determining the complex-valued field is performed non-iteratively.

[0190] 31. The method of clause 1, wherein the modulation function comprises a mask having a plurality of pinhole apertures, the plurality of pinhole apertures being at different orientations for different images of the sequence of images; and

[0191] The step of determining the complex-valued field comprises reconstructing the complex-valued field using iterative Fourier stack imaging reconstruction.

[0192] 32. The method of clause 1, wherein the modulation function comprises a binary representation of a desired complex-valued modulation.

[0193] 33. A method according to clause 32, wherein the binary representation of the expected complex-valued modulation comprises a Lee hologram representation of the expected complex-valued modulation.

[0194] 34. A method according to clause 33, comprising detecting three spatially separated orders, namely: one unmodulated order and two orders modulated by the expected complex-valued modulation and by carrier waves of mutually opposite signs.

[0195] 35. A method according to clause 33 or 34, wherein the expected complex-valued modulation comprises a 2 / 3π phase shift relative to a reference point.

[0196] 36. A method according to clause 35, wherein the expected complex-valued modulation further comprises an aberration correction component to correct aberrations in the imaging system.

[0197] 37. A measurement device for performing the method of any preceding clause, comprising:

[0198] an imaging system for imaging a field reflected from the sample;

[0199] at least one modulator at a Fourier plane of the imaging system for defining each modulation function; and

[0200] A detector at an image plane of the imaging system is used to capture each of said images.

[0201] 38. The metrology apparatus of clause 37, further comprising a second detector for imaging the Fourier plane prior to said modulation.

[0202] 39. A computer program comprising program instructions operable, when run on suitable apparatus, to perform the method of any of clauses 1 to 36.

[0203] 40. A non-transitory computer program carrier comprising a computer program according to clause 39.

[0204] 41. A processing device operable to run the computer program of clause 39.

[0205] 42. A measurement device for performing the method of any one of clauses 22 to 29, comprising:

[0206] an imaging system for imaging a field reflected from the sample;

[0207] at least one modulator at a Fourier plane of the imaging system for defining each modulation function; and

[0208] a detector at an image plane of the imaging system for capturing each of the images;

[0209] The imaging system comprises:

[0210] a first lens for focusing a point source onto the sample and capturing the zeroth order and at least one higher diffraction order,

[0211] a second lens for focusing the captured zeroth order and at least one higher diffraction order onto an intermediate image plane; and

[0212] a third lens that re-images the intermediate image plane; and

[0213] Wherein the modulator is located at the Fourier plane of the third lens.

[0214] 43. A measurement device according to claim 42, wherein the first lens comprises a separate lens having multiple parts separated by gaps, the multiple parts comprising a first part for focusing the point source onto the sample, a second part for capturing the at least one higher diffraction order, and a third part for capturing the zeroth order.

[0215] 44. The metrology apparatus according to clause 42 or 43, further comprising an illumination fiber or pinhole focused on the first lens as the point source.

[0216] 45. A measurement device according to clause 42, 43 or 44, wherein the modulator includes a pinhole aperture, which can be selectively opened and closed to define a first modulation function and a second modulation function, respectively, and the pinhole aperture is located at a position coinciding with the zeroth order at the Fourier plane, each of the first modulation function and the second modulation function otherwise passing through the full field at the Fourier plane.

[0217] Although specific reference may be made herein to the use of lithographic apparatus in IC manufacturing, it should be understood that the lithographic apparatus described herein may have other applications. Possible other applications include the manufacture of integrated optical systems, guidance and detection patterns for magnetic domain memories, flat panel displays, liquid crystal displays (LCDs), thin film magnetic heads, etc.

[0218] Although specific reference may be made herein to embodiments of the invention in the context of inspection or measurement devices, embodiments of the invention may be used in other devices. Embodiments of the invention may form part of a mask inspection device, a lithography device, or any device that measures or processes an object such as a wafer (or other substrate) or a mask (or other pattern forming device). The term "measurement device" may also refer to an inspection device or an inspection system. For example: an inspection device including an embodiment of the invention may be used to detect defects in a substrate or defects in a structure on a substrate. In such embodiments, the characteristic of interest of a structure on a substrate may be related to a defect in the structure, the absence of a particular portion of the structure, or the presence of an unwanted structure on the substrate.

[0219] Although specific reference is made to a "measurement device / tool / system" or an "inspection device / tool / system," these terms may refer to the same or similar types of tools, devices, or systems. For example, an inspection or measurement device including embodiments of the present invention may be used to determine characteristics of a structure on a substrate or on a wafer. For example, an inspection device or a measurement device including embodiments of the present invention may be used to detect defects in a substrate or defects in a structure on a substrate or on a wafer. In such embodiments, the characteristic of interest of a structure on a substrate may be related to a defect in the structure, the absence of a particular portion of a structure, or the presence of an unwanted structure on a substrate or on a wafer.

[0220] Although specific reference has been made above to the use of embodiments of the invention in the context of optical lithography, it will be appreciated that the invention is not limited to optical lithography and may be used in other applications, such as imprint lithography, where the context permits.

[0221] While the targets or target structures described above (more generally, structures on a substrate) are metrology target structures that are specifically designed and formed for measurement purposes, in other embodiments, the characteristics of interest may be measured on one or more structures that are functional components of a device formed on a substrate. Many devices have regular grating-like structures. The terms "structure," "target grating," and "target structure" as used herein do not require that the structure be provided specifically for the measurement being made. In addition, the pitch P of the metrology target may be close to the resolution limit of the optical system of the scatterometer, or may be smaller, but may be much larger than the size of a typical product feature made by a photolithographic process in the target portion C. In practice, the lines and / or spaces of the overlaid grating within the target structure may be made to include smaller structures that are similar in size to the product features.

[0222] Although specific embodiments of the present invention have been described above, it should be understood that the present invention may be implemented in a manner other than that described. The above description is intended to be illustrative rather than limiting. Therefore, it will be apparent to those skilled in the art that modifications may be made to the described invention without departing from the scope of the claims set forth below.

Claims

1. A method of determining a complex-valued field associated with a sample measured using an imaging system, comprising: obtaining image data associated with a series of images of the sample imaged at an image plane of the imaging system, and applying at least two different modulation functions in a Fourier plane of the imaging system to the image data; as well as The complex-valued field is determined from the image data based on the applied modulation function. 2 . The method according to claim 1 , wherein the at least two different modulation functions comprise a plurality of modulation function pairs, each modulation function pair comprising a modulation function that differs only in the disturbance region.

3. The method of claim 2, wherein each modulation function comprises a corresponding reconstruction region and a blocking region, the reconstruction region covering a different portion of the Fourier plane for each different pair of modulation functions.

4. The method according to claim 2 or 3, wherein the pair of modulation functions is implemented by a binary amplitude modulator.

5. A method according to claim 2 or 3, wherein the pair of modulation functions is implemented by a moving mask having a selectively closed aperture, the selectively closed aperture being used to provide a difference in the modulation functions at the perturbed area.

6. The method of claim 5, wherein the moving mask is a rotating mask and the selectively closed aperture is located at the axis of rotation. The method according to claim 2 , wherein the pair of modulation functions is implemented by a phase modulator. The method of claim 3 , wherein the perturbation region is located within the reconstruction region.

9. The method according to any one of claims 2, 3, 6, 7 and 8, wherein the perturbation region is located at a high intensity region in the Fourier plane.

10. The method according to any one of claims 2, 3, 6, 7 and 8, comprising the steps of: determining a plurality of partially reconstructed Fourier transforms by inverse Fourier transforming the series of images and determining differences between results for pairs of images corresponding to each of the plurality of modulation function pairs; combining the partially reconstructed Fourier transforms to obtain a reconstructed Fourier transform; as well as The complex-valued field is determined from the reconstructed Fourier transform.

11. The method according to any one of claims 2, 3, 6, 7 and 8, comprising the step of reconstructing the field at the disturbance zone by performing one or more of the following: inferring the amplitude at the disturbance region from the corresponding image in the Fourier plane; performing the method to reconstruct two or more disturbed regions and using one of the reconstructions to reconstruct the disturbed region of another; The field at the disturbed region is iteratively reconstructed using Fourier stack imaging.

12. The method of claim 1, wherein the modulation function comprises an amplitude grating and a reference pinhole; and the method comprises: capturing in a single image a plurality of diffraction orders diffracted by the grating; as well as The complex-valued field is determined from the imaged plurality of diffraction orders.

13. The method of claim 12, wherein the complex-valued field is determined from the image data using one of Fourier transform holography or parallel phase-shift holography.

14. The method of claim 12 or 13, wherein the reference pinhole is located at a high intensity region in the Fourier plane.

15. The method of claim 1, comprising defining at least three regions in the Fourier plane: a first reconstruction region, a second region, and a third region; reconstructing the field of the first reconstruction area from the image data, the image data being obtained from at least a first modulation function, the first modulation function being transmitted or reflected only in the first reconstruction area and at a plurality of reference points; The fields of the second region and the third region are reconstructed by the following steps: determining a first convolution of the fields of the first reconstruction area and the second area based on image data obtained from a second modulation function transmitted or reflected only in the first reconstruction area and the second area and a third modulation function transmitted or reflected only in the second area; determining a second convolution of the fields of the first reconstruction area and the third area based on image data obtained from a fourth modulation function transmitted or reflected only in the first reconstruction area and the third area and a fifth modulation function transmitted or reflected only in the third area; deconvolving the first convolution to reconstruct the field of the first reconstruction region and deconvolving the second convolution to reconstruct the field of the second region using the reconstructed field of the first reconstruction region; The reconstructed fields of the first reconstruction region, the second region and the third region are combined to determine the complex-valued field.

16. The method according to claim 1, comprising: constructing a plurality of linear equation systems from the image data, the image data comprising at least: a first image obtained from at least a first modulation function corresponding to a full field to be reconstructed, a second image obtained from a second modulation function corresponding to a first half of the full field, and a third image obtained from a third modulation function corresponding to a second half of the full field; and The plurality of linear equations are solved non-iteratively using double-blind Fourier holography.

17. A method according to claim 16, wherein the at least two different modulation functions include a first modulation function for obtaining a first image of an image pair and a second modulation function for obtaining the second image of the image pair, and wherein the only substantial difference between the modulation functions is that the second modulation function blocks selected higher diffraction orders and the first modulation function does not block selected higher orders.

18. The method of claim 17, wherein each of the first modulation function and the second modulation function blocks less than 10% or 5% of an area defined by a Fourier plane.

19. A method according to claim 17 or 18, wherein the first and second modulation functions are configured to block a minimum amount of diffracted radiation in addition to selected higher orders being blocked by the second modulation function.

20. The method according to claim 17 or 18, further comprising: A difference image of the first image and the second image is determined for each of the pairs of images, each of the difference images describing the image solely in terms of linear imaging terms.

21. The method of claim 20, comprising capturing a plurality of said image pairs, each image pair being associated with one of a plurality of focus levels; and determining a difference image for each image pair to obtain a through-focus series of difference images; and By performing a linear fit of two unknowns on the difference images of the through-focus series, the twin image is separated from the regular image in each of the difference images determined.

22. The method of claim 1, wherein: two different said modulation functions differ only in: the selective opening and closing of a reference pinhole defining a perturbation region, said perturbation region being aligned in said Fourier plane with the zeroth order of reflected radiation from said sample; and The determining of the complex-valued field is performed by a self-referenced holographic method using the zeroth order as a reference.

23. The method of claim 22, wherein each of two different said modulation functions passes substantially the entire field of said Fourier plane, except that said perturbation region is blocked in only one of the two different said modulation functions.

24. The method according to claim 22 or 23, wherein the determining step comprises: determining a difference between a first measurement corresponding to a first one of two different said modulation functions and a second image corresponding to a second one of the two different said modulation functions; and The result is inverse Fourier transformed to obtain the reconstructed complex field.

25. The method of claim 24, wherein the determining step further comprises clipping a twin field from the reconstructed complex field.

26. The method of claim 24, further comprising: obtaining a third measurement corresponding to a third modulation function that blocks the entire field except for the disturbance region; and using the third measure to correct the reconstructed complex field for the effects of the finite size of the disturbance region.

27. The method according to any one of claims 22, 23, 25 and 26, further comprising: focusing a point source onto the sample, focusing the zeroth order and at least one higher diffraction order at an intermediate image plane; as well as The modulation function is applied at the Fourier plane of a lens which re-images the intermediate image plane.

28. A method according to any one of claims 22, 23, 25 and 26, comprising using a separate objective lens to illuminate the sample and capture the zeroth order and at least one higher diffraction order; wherein the separate objective lens includes a plurality of parts separated by gaps, the plurality of parts including a first part for focusing the illuminating radiation onto the sample, a second part for capturing the at least one higher diffraction order and a third part for capturing the zeroth order.

29. The method of any one of claims 22, 23, 25 and 26, wherein the reference pinhole is apodized.

30. A method according to any preceding claim, wherein for at least most of the complex-valued fields, the step of determining the complex-valued field is performed non-iteratively.

31. The method of claim 1, wherein the modulation function comprises a mask having a plurality of pinhole apertures, the plurality of pinhole apertures being in different orientations for different images in the sequence of images; and The step of determining the complex-valued field comprises reconstructing the complex-valued field using iterative Fourier stack imaging reconstruction.

32. The method of claim 1, wherein the modulation function comprises a binary representation of a desired complex-valued modulation.

33. The method of claim 32, wherein the binary representation of an expected complex-valued modulation comprises a Lee hologram representation of the expected complex-valued modulation.

34. The method of claim 33, comprising detecting three spatially separated orders: one unmodulated order and two orders modulated by said expected complex-valued modulation and by carrier waves of mutually opposite signs.

35. A method according to claim 33 or 34, wherein the expected complex-valued modulation comprises a 2 / 3π phase shift relative to a reference point.

36. The method of claim 35, wherein the expected complex-valued modulation further comprises an aberration correction component for correcting aberrations in the imaging system.

37. A metrology apparatus for performing the method of any preceding claim, comprising: an imaging system for imaging a field reflected from the sample; at least one modulator at a Fourier plane of the imaging system for defining each modulation function; as well as A detector at an image plane of the imaging system is used to capture each of the images.

38. The metrology apparatus of claim 37, further comprising a second detector for imaging the Fourier plane prior to the modulation.

39. A computer program comprising program instructions operable, when run on suitable apparatus, to perform a method according to any one of claims 1 to 36.

40. A non-transitory computer program carrier comprising a computer program according to claim 39.

41. A processing device operable to run the computer program of claim 39.

42. A measurement device for performing the method according to any one of claims 22 to 29, the measurement device comprising: an imaging system for imaging a field reflected from the sample; at least one modulator at a Fourier plane of the imaging system for defining each modulation function; as well as a detector at an image plane of the imaging system for capturing each of the images; The imaging system comprises: a first lens for focusing a point source onto the sample and capturing the zeroth order and at least one higher diffraction order, a second lens for focusing the captured zeroth order and at least one higher diffraction order at an intermediate image plane; as well as a third lens that re-images the intermediate image plane; and Wherein the modulator is located at the Fourier plane of the third lens.

43. A measurement device according to claim 42, wherein the first lens comprises a separate lens having multiple parts separated by gaps, the multiple parts comprising a first part for focusing the point source onto the sample, a second part for capturing the at least one higher diffraction order, and a third part for capturing the zeroth order.

44. The metrology apparatus of claim 42, further comprising an illumination fiber or pinhole focused on the first lens as the point source.

45. A measurement device according to claim 42, 43 or 44, wherein the modulator includes a pinhole aperture, which can be selectively opened and closed to define a first modulation function and a second modulation function, respectively, and the pinhole aperture is located at a position coincident with the zeroth order at the Fourier plane, and each of the first modulation function and the second modulation function otherwise passes through the full field at the Fourier plane.

Images